







Hexagonal pyramid bevel angles 
20160930 

From Peter: I have seen your response to a similar question from Steve which Chris and Harley responded to, however I am not familiar with some of the terms. Is there a formula that I can enter my details in which will give me the specific angles I require. The item I am constructing is much larger than the one you responded to previously. Thank you for any assistance you are able to provide. Answered by Penny Nom. 





The dimensions of a rectangle 
20160831 

From Hazym: How do I find the length(which is 15m longer than the breadth) and the breadth of a rectangle just by its perimeter which is 70 m? Answered by Penny Nom. 





The circumcentre of a triangle 
20160728 

From Raj: If the vertices of triangle ABC are A(4,1) B(1,2) C(4,3) then find coordinates of circumcentre of triangle Answered by Penny Nom. 





The dimensions of a rectangle 
20160725 

From Krunox: A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width. Answered by Penny Nom. 





The number of sides of a polygon 
20160723 

From Shriya: All the angles of a polygon are either 155° or 140°.
There are twice as many angles of 155 °or 140°.
Find the number of sides of the polygon Answered by Penny Nom. 





A congruence theorem for two right angled triangles 
20160717 

From Sayari: Hello.
Is it possible for two right angled triangles to have the same length of base and height and a different hypotenuse? If not so, then why in the congruence criteria RHS the hypotenuse is given more importance? It can also be like 'two triangles are congruent if they are right angled and have the same base and height.'
Thank You. Answered by Penny Nom. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





A trough with a triangular cross section 
20160521 

From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom. 





sin 2x  sin x = 0 
20160424 

From lilly: sin 2x  sin x = 0 0 Answered by Penny Nom. 





A triangle inscribed in a circle 
20160422 

From Olyana: I am struggling with this question! Help!
So, there is a circle. In the circle, there is an equilateral triangle inscribed.
Each side of the triangle is 20. There is no other info given, other than
the triangle is inscribed in the circle and the sides of the triangle are 20.
I am supposed to find the radius of the circle! Please help! Answered by Penny Nom. 





External and interior angles of a regular polygon 
20160419 

From pearl: a polygon has n sides.The exterior angle is 8 times the interior angle
find the value of the interior angle
find the value of n Answered by Penny Nom. 





The area and the perimeter of a rectangle 
20160412 

From kimberly: is there a relationship between the are and the perimeter of a rectangle?
explain. Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20160325 

From NIHAL: A isosceles triangle is inscribed in a circle having sides 20cm,20cm,30cm. find the radius of circle Answered by Penny Nom. 





The perimeter of a rectangle 
20160317 

From Linda: Noel correctly adds the length of three sides of a rectangle and gets 88 cm her brother Ryan correctly adds the lengths of three sides of the same rectangle and gets 80cm. What is the number of cm in the perimeter of the rectangle Answered by Penny Nom. 





The sides of a triangle 
20160315 

From Hitarth: Why we cannot construct a triangle ofngiven sides 5cm,5cm and 10cm? Answered by Penny Nom. 





Angles 
20160312 

From Laurynn: What are angles in general (please include the 'angle of incline')
Thank you
Laurynn Answered by Penny Nom. 





The area of a rectangle 
20160303 

From Lucas: The area of a rectangle is given by A=x2+18x+72
use factoring to find an expression for the dimensions of the rectangle.
if the area of the rectangle is 7 square feet, what are the possible values of x?
what are the dimensions of a rectangle? Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





The interior and external angles of a regular polygon 
20160217 

From percy: a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle .
1.find the size of each exterior angle
2.calculate the value of n Answered by Penny Nom. 





The height of a triangle 
20160203 

From Brooklyn: How do I figure out the height of a triangle when it only tells me the base of he triangle? And vice versa. Answered by Penny Nom. 





Consecutive angles of a parallelogram 
20160128 

From Hanna: The consecutive angles of a parallelogram measures Answered by Penny Nom. 





The perimeter of a triangular plot of land 
20160111 

From Janelle: I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off? Answered by Penny Nom. 





The area of a rectangle 
20160108 

From ranjan: if we make a rectangle with a 100cm of wire, then its area will be? Answered by Penny Nom. 





The angles of a triangle 
20151217 

From Faith: Does the measure of angle determine the length of its side? For example two angles are congruent then the sides are also congruent because from my understanding the angle determine the shape of triangle. Answered by Penny Nom. 





The dimensions of a rectangle given its area and aspect ratio 
20151213 

From colum: Can you work out the length and width of a rectangle where you know only the area and aspect ratio Answered by Penny Nom. 





The sweep angle of a video camera 
20151125 

From Franc: a television camera is 30ft from the sideline of a basketball court 94 ft long. The camera is located 7 ft from the mid court. through what angle must it sweep in order to cover all action on the court? Answered by Penny Nom. 





The angle at the vertex of an isosceles triangle 
20151125 

From Karan: I have been given an isosceles triangle. the Top angle is what i have to find out and the two sides adjacent to it are both 4.9 cm. i have been told that the area of the triangle is 4 cm^2. i have no idea how to work this out, any ideas? Answered by Penny Nom. 





The measure of an angle in terms of its complement 
20151122 

From Pam: Can you please help me so I can help my daughter the equation is the measure of angle v is 4 time the measure of its complement what is the measure of angle v when the equation is 4x+x=90 Answered by Penny Nom. 





The length of a rectangle 
20150926 

From Tris: Hi,
I'm trying to figure out the length of a rectangle but i forgot how. So, the width is
5cm and the perimeter is 34cm. Answered by Penny Nom. 





The dimensions of a rectangle 
20150925 

From Erick: A rectangular strip of land has a perimeter of 124meters and an area of 385 square meters. Find its possible dimensions Answered by Penny Nom. 





The length of a shadow 
20150801 

From maaz: Hello
I am having trouble with this question:
Lizzie, who is 6 feet tall, stands in her driveway at night, exactly
24 feet from the base of a spotlight, and casts a shadow that is 12
feet long if her friend Hannah who is 5 feet tall decides to stand
next to lizzie how long will her shadow be? Answered by Penny Nom. 





The area of an isosceles triangle 
20150611 

From Pradipta: Find the area of an isosceles triangle having two equal sides of 20 cm each and angle between them 45 degree ? ( solve without trigonometric function). Answered by Chris Fisher. 





An equilateral triangle inscribed in a circle 
20150611 

From Casey: I have an equilateral triangle inscribed in a circle  this triangle
has been bisected to give me 2 right triangles. I know the length
of the line bisecting the equilateral triangle is 36 inches. How do
I figure out the circumference of the circle and the length of the
sides of the equilateral triangle? Answered by Penny Nom. 





The perimeter of a rectangle 
20150528 

From Imran: The length of a rectangle is x+3 centimetres.
The width of the rectangle is x1 centimetres.
Find an expression in terms of x for the perimeter of the rectangle.
The perimeter of a rectangle The perimeter of a rectangle
Give your expressions in it's simplest form.
The perimeter of a rectangle The perimeter of a rectangle
Thank You. Answered by Penny Nom. 





An isosceles right triangle 
20150517 

From Ari: In a 454590 triangle find the ratio of a leg to the hypotenuse Answered by Penny Nom. 





An octagonal frame around a pool 
20150517 

From James: I have a 20' pool and need to put a frame around it using 2by 4 what r the lengths and angle cuts Answered by Penny Nom. 





An angle of depression problem 
20150514 

From haxir: find the height of the balloon directly above a town if the measure of angle of depression of another town 5km from the first town is 20°!6` Answered by Penny Nom. 





Folding a rectangle to preserve the aspect ratio 
20150509 

From Anna: If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles? Answered by Penny Nom. 





A triangle inscribed in a circle 
20150507 

From R2D2: A triangle is inscribed in a circle of radius 10. If two angles are 70 degrees and 50 degrees find the length of the side opposite the third angle? Answered by Chris Fisher. 





A square and a rectangle 
20150501 

From nick: why is the area of a square of a given circumference greater than the area of a rectangle with the same circumference ? Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20150323 

From Rachel: Triangle ABC is an isosceles triangle inscribed in circle O. If each leg of the triangle is 13cm and the altitude to the base of triangle ABC is 5cm, find the radius of the circle. Answered by Penny Nom. 





The height of an equilateral triangle 
20150312 

From anna: I am anna and i am in 7th grade.
i am trying to find the height of and equilateral triangle, all sides equaling 4 inches Answered by Penny Nom. 





Angles of elevation and depression 
20150308 

From Timmy: Joel is walking down a street and sees a 115 ft tall building in front of him. He stops 190 feet from the base of the building at the tip of the building's shadow. Round answers to three decimal places.
A. If there was a piece of rope from the top of the building to Joel, how long would it be?
B. What is the angle of elevation from Joel to the top of the building?
C. Margaret says that she could find the angle of depression from the top of the building to Joel by subtracting the angle of elevation from 90°. Is she correct? Explain. Answered by Penny Nom. 





A man is standing on top of a building 
20150306 

From kiki: a man of height 1.5m standing on top of a building of height 48.5m views another building across the square. he observe that the angle of depression of the bottom of the building is 40 degrees and the angle of depression of the top of the building is 5 degrees. Both buildings stand on the same level
a) calculate the distance of the man from the base of the building across the square measured along the line of sight Answered by Penny Nom. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





The height of a building 
20150120 

From Emily: A man 2m high observes the angle of elevation to the top of the building to be 70 degrees. And the angle of depression to the bottom of the building to be 19 degrees. How tall is the building? Answered by Robert Dawson. 





The length of a roll of paper 
20150112 

From Peggy: roll of paper 3ft wide and roll equals 500 sq ft how long would the roll be? Answered by Penny Nom. 





An isosceles triangle 
20141231 

From ahmadmahmoud: an isoseles triangle is such that each of the base angles is twice the vertical angle.Find the angles of the triangle Answered by Penny Nom. 





A right triangle 
20141213 

From Katie: the shorter leg of a right triangle measures 2 feet less than the longer leg. the hypotenuse measure 10 feet. find all three sides Answered by Penny Nom. 





Cutting a hexagon with a sliding miter saw 
20141123 

From Joseph: I need the angles in degrees for a hexagon one side is 18inches on the outside the problem I am having is in the angle of the cut and I am using a sliding miter saw which only goes from0 degrees to 45 degrees so I need help in getting the angle of the cut Answered by Harley Weston. 





Building an 8 sided box 
20141014 

From Michael: I want to build an 8 sided box. The North, East, South, and West sides I want them to be 4 feet in length.
The NE, SE, SW, and NW sides I want to be 2 feet in length. What angles do I need to cut my angles.
Thanks Michael Answered by Penny Nom. 





A rectangle and a triangle 
20140927 

From rajesh: The perimeter of a rectangle is equal to the perimeter of a rightangled triangle of height 12 cm if the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle? Answered by Penny Nom. 





A wire is bent to form a right triangle 
20140925 

From Lorena: A wire 24 dm is bent to form a right triangle. The ratio of the shorter leg to the hypotenuse is 3:5. Find the length of the longer leg? Answered by Penny Nom. 





The perimeter and diagonal of a rectangle 
20140910 

From niniha: the perimeter of a rectangle is 68cm.if the diagonal is 26, find its dimensions Answered by Penny Nom. 





Interior angles in a parallelogram 
20140830 

From xavier: so, one of my math homework questions requires me to know how to find out how to find the interior angles in a parallelogram, the question is, "how many interior angles does a parallelogram have?" Answered by Penny Nom. 





The perimeter of a triangle 
20140821 

From Phyllis: What is the perimeter of a five acre triangle with one side being 250 feet and the second side would be at a 90 degree angle.
Thank you. Answered by Penny Nom. 





A barge of triangular cross section 
20140818 

From tushar: a barge of triangular cross section is 20m long 12 m wide and 6m deep.its floats in SW at a draft if 4m find its displacement Answered by Penny Nom. 





The dimensions of a rectangle 
20140803 

From Jamaica: if the perimeter of a rectangle is 30m and its area is 56 m2.find its length and width? Answered by Penny Nom. 





A ladder against a wall 
20140709 

From thabo: A ladder 6.5m long,leans against a wall so that the top of the ladder is 4.8m from the ground.what is the angle of elevation of the ladder to the top of the wall Answered by Penny Nom. 





The width of a rectangle 
20140702 

From john: if the area of a rectangular field is 90 sq. m and its length its is 19 m find its width Answered by Penny Nom. 





A triangle on the surface of the Earth 
20140626 

From Christine: A, B and C are three towns, the bearing of B and C from A being 310 degrees and 220 degrees, and their distances from A are 510km and 700km respectively. Find the bearing of B from C to the nearest minute. Answered by Robert Dawson. 





An equilateral triangle with vertices in 3 parallel planes 
20140531 

From prajay: How to construct an Equilateral Triangle whose vertices lie on three
parallel lines, if the distances of two lines are 'a' and 'b' units
from the middle line.What is the length of the side of the
Equilateral Triangle ? Answered by Chris Fisher. 





A circle a square and a rectngle 
20140512 

From mazhar: suppose the length and breadth of the rectangle are 5 cm and 10 cm respectively and M is a point along the corner of the circle. what is the radius of the circle?(diagram is given..but i didn't mention it..actually the diagram looks like a circle inscribed in a square and the right bottom corner one rectangle will be given ,it is touches to circle at a point M that I've already mentioned and the dimensions of that rectangle also I've mentioned) please help me out.. Answered by Penny Nom. 





The length of a shadow 
20140509 

From vijay: A girl of height 80 cm is running away from the base of a lamppost at a speed of 2 m/s. If the lamp is 4 m above the ground, find the length of her shadow after 5 seconds. Answered by Penny Nom. 





Solve for theta 
20140425 

From ALASTAIR: Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta.
Substituting for cos2th either 12sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please? Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





The sides of a triangle 
20140406 

From Michael: I am supposed to sove for the length of side "b" of an irregular triangle. I am given the following:
Side a: 65'
Side b: Find this length
Side c: 50'
Angle A: unknown
Angle B: unknown
Angle C: 52 degrees
I am supposed to use the law of cosines to solve for side "b" and my teacher
says there is no mistake in the "givens" for the problem. I do not see how
this can be done using the law of cosines and i have not figured out how to sove for
angle B to use the law of cosines. Answered by Penny Nom. 





Shadows of a father and son 
20140402 

From esada: the father and son cast a shadow of 11 feet and 8 feet,respectively if the son is 4'8'' in height,how tall is the father? Answered by Penny Nom. 





Is this a right triangle? 
20140401 

From amina: decide whether or not the following points are the vertices of right triangle (9,2),(1,2),(9,11) Answered by Penny Nom. 





The faces of a triangle 
20140324 

From Westun: Your answer says that a triangle has 0 faces but isn't
the part of the shape you see the face!? Because i am having trouble
with that so could you help me!
thanks! :) Answered by Penny Nom. 





A circle inscribed in a right triangle 
20140316 

From akshaya: A circle with centre O and radius r is inscribed in a right angled triangle ABC. If AB=5 cm, BC=12 cm and < B=90*, then find the value of r. Answered by Penny Nom. 





A chord length of 2 cm 
20140313 

From prema: I am having only chord length as 2cm. how to find arc length and degree Answered by Penny Nom. 





The angle of depression 
20140308 

From Ranger_minor: A woman of height 1.4 metres standing
on the top of a building 34.6 metres high
views a tree some distance away.
she observes that the angle of depression of the bottom of the tree
is 35 degrees and the angle of depression of the top of the tree
is 29 degrees.
assume that the building and the tree are on level ground :
1). calculate the distance of the woman
from the top of the tree measured along her line of sight. Answered by Penny Nom. 





What are the possible lengths of the hypotenuse? 
20140307 

From audrey: The three sides of a right angles triangle measure x2, x+5, and 2x1 in length.
What are the possible lengths of the hypotenuse?
... I'm doing the equation c2=a2+b2 and subbing in the numbers but nothing makes sense Answered by Penny Nom. 





A circle graph 
20140306 

From Caitlyn: I need to find the measure of the central angle that represents the amount of time spent on each activity.
My question includes a circle graph with the following: Sleep 31%, Other 15%, Entertainment 18%, Errands 7%,
Work 20%, and Food 9%. Answered by Penny Nom. 





A triangle has angels in the extended ratio of 2:5:8 
20140206 

From Rubina: a triangle has angels in the extended ratio of 2:5:8. find the measure of
all three angles? Answered by Penny Nom. 





A rectangle inscribed in a circle 
20140110 

From Marian: A 16 cm by 12 cm rectangle is inscribed in a circle. Find the radius of the circle. Answered by Penny Nom. 





A scalene triangle 
20140107 

From cherry: Hi
I have been given a scalene triangle of sides 
8m, 6m, and 10m ..
Please help me to find out the area and help me to find out the height .. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20140106 

From Anonymous: An equilateral triangle with sides 6 inches is inscribed in a circle. What is the diameter of the circle? Answered by Penny Nom. 





The perimeter of a rectangle 
20131024 

From sana: if the length is given 70 m and the breadth is given as 40 m find the perimeter of the rectangle Answered by Penny Nom. 





A triangle problem 
20131002 

From raneem: ABC is a triangle in which : BC=20cm. M(<B) =29 and m(<C)=73 . D is the midpoint of BC
Find the length Of AB and AD approximated to 2 decimal places Answered by Penny Nom. 





Constructing a triangle 
20130822 

From Nazrul: The base, the difference of the angles adjoining the base and the sum of the other
two sides are given. How can I draw the triangle?
Please help me. Answered by Chris Fisher. 





Similar rectangles 
20130817 

From Mattie: The dimensions of a rectangularshaped picture frame are 14 inches long and four inches wide. Which dimensions below represent another frame that i geometrically similar>
a. l=49 in. and w=14in.
b. l=7in and w=3in
c. l=21in and w=8in
d. l=24in and w=14in
thanks Answered by Penny Nom. 





Using trig to find the height of a hill 
20130814 

From Anna: From the top of a hill, the angles of depression of two successive milestones on a level road, which leads straight away from the hill, are 5degrees and 15degrees respectively. Fine the height of the hill.
Suggestion: BE is drawn perpendicular to AD. Find BE, then BD, finally CD.
Thanks :) Answered by Penny Nom. 





A triangle construction 
20130727 

From Nazrul: Two angles and the difference of the lengths of their opposite sides of a
triangle are given. How can I draw the triangle.
Please help me. Answered by Chris Fisher. 





The angle of elevation of the sun 
20130703 

From Maurice: A vertical pole with a length of 7m cast a shadow with a length of 5m. Calculate the angle of elevation of the sun and include a diagram. Answered by Penny Nom. 





An isosceles tiangle 
20130616 

From Izzy: what's the height of an isosceles triangle which has a base of 50 m, and both of the other sides are 25 m? Answered by Penny Nom. 





A kennel for a beagle 
20130603 

From david: Hi, I'm building some beagle kennels and I am in need of help with an angle problem. I need to place a roof on my kennel with a drop of 2inches across 3ft 10inches. the posts on the right side will be 5ft and the post on the left will be 4ft 10in. the posts are 4x4 and the space to be covered is 3ft 10in from the outside of the 4x4. Please help, thanks. Answered by Penny Nom. 





siin (A) and sin (A/2) 
20130509 

From shanaia: given that sin A=4/5 and A is obtuse.find sin (A/2) Answered by Penny Nom. 





A triangle and an incircle 
20130509 

From Max: On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this. Answered by Chris Fisher. 





Drawing a pentagon 
20130506 

From jacob: hello. i am trying to draw a template for a project. but i don't have a
protractor. i'm trying to draw a normal pentagon with 2cm sides. what
i'm trying to figure out is the distance in centimeters from point a, to c,
in a straight line. this is needed so that i can measure and create the
shape without a protractor, and keep the angles and sides correct.
if you can help me with the measurement, or help me another way,
any help would be greatly appreciated. thank you. Answered by Penny Nom. 





The area of a right triangle 
20130410 

From derek: The legs of a right triangle measure 4 and 6 inches. The area of the triangle is Answered by Penny Nom. 





The area of an isosceles right triangle 
20130330 

From Michelle: We have a triangle it is a right isosceles. The sides touching the right angle are 10 cm. They hypotenuse is 14.1 (the base) we are trying to find the height of this so we can figure out the area of a shaded sector of a circle. Answered by Chris Fisher. 





A shortest distance problem 
20130328 

From LYNDELL: I have a right triangle and know the length of all sides. How do I calculate the shortest distance from the vertex of the 90 degree angle to the hypotenuse? Answered by Penny Nom. 





Trigonometry 
20130323 

From Tizoc: I am in a trig class and I have a conflict. When solving the length of a side, I know what trig function to use, but I do not know what angle to use in a calculator. To make this a little more understandable, if I have all the angles available in a right triangle and I use the tangent function, how do I know what to use?
Heres what I do not know what to put in my calculator: Tan(?)
Thanks in Advance! Answered by Penny Nom. 





The dimensions of a rectangle 
20130319 

From stephanie: the length of a rectangle is 5m more than twice its width, and the area of the rectangle is 88m^2 find the demensions of the rectangle Answered by Penny Nom. 





Fencing a parcel of land 
20130311 

From Koleen: How much fencing do I need for an 56,850 parcel of land for a 15 stable horse barn Answered by Penny Nom. 





The area of a rectangle 
20130129 

From Bali: if the length of the
rectangular field is decreased by 5m,
its area is decreased by 70 sqm. if the
width is increased by 6m, the area is
increased by 180 sqm. determine the
length and width of the rectangular
field? Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20130117 

From Nicole: How do you find the shaded region of a circle if an unshaded equilateral triangle in inscribed in it. The only other things I know about the problem are that the side lengths of the equilateral triangle are 14 inches. Answered by Penny Nom. 





The side lengths of a triangle 
20130107 

From Katie: How do I find the side lengths of a triangle knowing the base and its height?
Thank you, Answered by Penny Nom. 





The perimeter of an equilateral triangle 
20121214 

From shreyaarora: if the area of on equilateral triangle is 24/3cm,then what is its perimeter Answered by Penny Nom. 





The angles of elevation and depression 
20121203 

From Chelsey: a person on a balcony of one building looks towards a second building. if the angle of elevation to the top of the second building is 25 degrees, the angle of depression to the bottom of the second building is 17 degrees, and the balcony of the first building is 22 feet above the ground, what is the height of the second building? Answered by Penny Nom. 





A circle inscribed in a triangle 
20121128 

From Angie: Circle O is inscribed in triangle ABC. Angle A = 50 and angle B = 60. Find arc XY in dgrees Answered by Penny Nom. 





The area of a triangle given its vertices 
20121127 

From elizabeth: how to calculate the area of a triangle using points ABC a (2,5) b ( 4,3) c ( 6, 1) Answered by Penny Nom. 





Two sides of a triangle 
20121125 

From Nazrul: In the triangle ABC, AB>AC and the bisector AD of angle BAC intersects BC at D. How can I prove that angle ADB is an obtuse angle. Answered by Penny Nom. 





Two congruent circles in a rectangle 
20121020 

From Alexander: Have you ever solved a problem, in which you have a rectangle, from which you need to cut the largest two circles of equivalent diameter? I bisected a rectangle diagonally, but the circles, while tangent to two of the sides, are not tangent to eachother. Can you devise a method for two equivalent circles, that are tangent to two sides, are also to eachother?
Take for example a piece of paper, Each if the two largest circles has a diameter that is greater than the distance to the midpoint of the diagonal bisector of the rectangle. Answered by Chris Fisher. 





The degree measure of the central arc of a circle 
20121017 

From Crystal: On a circle with radius of 12 cm is an arc of length 20 cm. What is the degree measure of the central angle used to make this arc? Answered by Penny Nom. 





The height of a triangle 
20121017 

From Brian: the base of my triangle is 12 metres and the two sides are 8.45 metres
can you help me find the height of the triangle Answered by Penny Nom. 





The perimeter of a rectangle 
20120919 

From aretha: calculate the perimeter of a rectangle with the long side 462ft x 9inches and the short side 50% less. Answered by Penny Nom. 





The dimensions of a rectangle 
20120912 

From Becky: A rectangle has an area of 48 square inches and perimeter of 32 inches. Find the dimensions of the rectangle. Answered by Penny Nom. 





An equilateral triangle and a regular hexagon in a circle 
20120911 

From Heidemarie: The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle. Answered by Penny Nom. 





The hypotenuse 
20120906 

From Jeevan: how can i find the height and base of a right angle triangle if i have the hypotenuse only ? Answered by Penny Nom. 





The area of a rectangle 
20120831 

From mario: The area of a triangle when on side is x and the other is x+6 Answered by Harley Weston. 





Problem solving 
20120815 

From Sugavanas: If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle. Answered by Penny Nom. 





Two altitudes of a scalene triangle 
20120813 

From grace: Two of the altitudes of a scalene triangle ABC have length 4 and 12. If the length of the third altitude is also an integer, what is the biggest that it can be? Justify all of your conclusions. Answered by Chris Fisher. 





Three right triangles 
20120726 

From Jora: I am having a lot of difficulties with this question.
Name: Jora
Subject: Math
Who are you: Student Answered by Chris Fisher. 





The area of a rectangle 
20120724 

From michael: the dimension of the rectangle are (x+5) and (x3) find its area Answered by Penny Nom. 





A truncated cone: the central angle 
20120717 

From Tom: I have researched several sites, including this one and am fairly confident I can do the calculations required to produce the two radii and the slant height for a truncated cone.
I a somewhat confused by the central angle. Some sites indicate that it should never exceed 180 degrees while others do not. Different examples on your site seem to use this in two different ways in constructing a truncated cone.
Sometimes the angle seems to indicate the section to be removed, while in other examples the angle seems to indicate the section to be saved. Since the two angles will always total 360 I am confused about how to use the info to
calculate the minimum rectangle required to contain the pattern. I'm guessing that in some cases I may need to use the chord or sagitta to determine the desired height and width of the material. Any help is greatly appreciated.
Thank you.
Tom Answered by Penny Nom. 





The angular elevation of the sun 
20120714 

From VINEET: WHAT IS ANGULAR ELEVATION OF THE SUM Answered by Penny Nom. 





The height of an isosceles triangle 
20120710 

From ken: I am trying to determine the various heights of an isosceles triangle, if each has the same base dimension and varies in the degree of the base (equal) angles. What is the method to do this?
As an example, of the base is 10, and the two equal angles are each 45 degrees, what is the height? With the same base (10), but with the two equal angles at 60 degrees, what is the height? And with the same base (10) and the two equal angles at 75 degrees, what would be the height?
I know how to calculate the degrees of the third angle (add the degrees of the known angles, and subtract from 180); but am unsure if that is needed for figuring the overall height.
And to be clear; I am not looking for the length of the sides of the triangle, but the height from the base to the top point.
Thank you! Answered by Chris Fisher. 





An octagonal sandbox around a pool 
20120612 

From Linda: My pool is 15 feet across and it is round.
How do I measure to cut wood to build a sandbox around it? was thinking it will look like an octagon.
Thanks Answered by Harley Weston. 





Finding the circumcentre 
20120524 

From Glen: Hi,
I'm having trouble finding the circumcentre of these 3 coordinates A(1,1) B(10.5,1) and C(6,6).
I understand what circumcentre is but I cannot work out where it is.
Thanks very Much,
Glen Answered by Chris Fisher. 





The area of a triangle 
20120517 

From Emilee: hi. How do i find the area of a triangle if the vertices are (3,0) (2,2) and (3,0). I graphed it and it came out a triangle. How do I find the area of it in an easy way? Answered by Penny Nom. 





Drawing an isosceles triangle 
20120510 

From Nazrul: How can I draw an isosceles triangle whose each angle adjacent to the base is twice the vertex angle? Answered by Chris Fisher. 





The maximum distance from the vertex of a triangle 
20120502 

From David: There are three towns A,B,and C, equidistant apart.
A car is 3 miles from town A, and 4 miles from town B.
(ie, somehwere outside of the triangle which the three towns form)
What is the maximum distance that the car can be from town A?
This was asked as quiz question in my local pub last Sunday.
The answer is 7. How do I prove it?
Best regards. David in Denton. Answered by Robert Dawson and Chris Fisher. 





The dimensions of a rectangle 
20120430 

From Nikki: Name the dimensions of a rectangle that has the same area as this triangle?
I found the area of the triangle, which is 30. What do I have to do in order to complete this math problem? Answered by Penny Nom. 





Third side of a irregular triangle. 
20120427 

From Darya.: How to find third side of irregular triangle if c = 17m, b = 28m and area S = 210m^2. Answered by Penny Nom. 





A circle inscribed in a triangle inscribed in a circle 
20120426 

From Maty: How do i find the area of a triangle inscribed a circle while another smaller circle is circumscribed by the same triangle and the radius is 8. Answered by Chris Fisher. 





The circumcentre and orthocentre of a triangle 
20120425 

From Nazrul: The circumcentre and orthocentre of a triangle is given. A point on a side of the triangle
given. A vertex of the triangle on the circumcircle is also given.
How can I draw the triangle?
Please Help me.
Thank you for answering my previous questions. Answered by Chris Fisher. 





How to find the base length of a isosceles triangle if only the sides are given? 
20120425 

From aqilah: how to find the base length of a isosceles triangle if only the sides are given? Answered by Chris Fisher. 





A puzzle with a triangle and 57 
20120425 

From sharon:
Question from sharon, a parent:
We have been battling with this for days and cant find any solution 
Using each of the following numbers once, fill all the spaces in the triangles so that each side of the triangle adds up to 57
numbers are 11,12,13,14,15,16,17,18,19
diagram is 
Any ideas ? this has to be in in just over 24 hrs ......help! Answered by Chris Fisher. 





The area of a right triangle 
20120403 

From Shelli: How do you find the area of a right triangle if you only know that the hypotenuse is 10 and that the base and height are unknown but are equal? Answered by Penny Nom. 





A circle drawn around a equilateral triangle 
20120401 

From BIMAL: what is the diameter of a circle drawn around a equilateral triangle of size 6 cm Answered by Penny Nom. 





Angle measures 
20120321 

From jogiboy: how can i get the sine theta if the given is 3.14/3 Answered by Penny Nom. 





Gravel, sand, cement and an equilateral triangle 
20120321 

From saheed: how many tonnes of gravel and sand,bags of cements will be required to concrete 5feet depth/deep of 4feet equilateral triangle? Answered by Harley Weston. 





Forming a triangle from 3 line segments 
20120315 

From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom. 





The dimensions of a rectangle 
20120313 

From irvyn: if you are only given the area and the perimeter how do you find the dimension? Answered by Penny Nom. 





The area and perimeter of a rectangle 
20120301 

From RAJIB: PEREMETER OF A RECTANGLE IS 24. FIND THE AREA ? Answered by Penny Nom. 





The height of an equilateral triangle 
20120229 

From Carley: Hi my name is Carley. I am an 8th garder. What us the height of an equilateral triangle si the sides are 18 cm? Answered by Penny Nom. 





A road around a garden 
20120207 

From Manu: Inside a square garden of side 158m, a road 4m wide is built all around. What is the area of the remaining part of the garden? Answered by Penny Nom. 





The dimensions of a rectangle 
20120131 

From Dazz: Hi I was wondering how to find the length of a rectangle if you know the area is 484 square inches And the length is 10 square inches or 22 square inches?
Thanks~Dazz Answered by Penny Nom. 





The area of a triangle 
20120127 

From mary: I have a scalene triangle and the base is 33m, side is 52m and the unparallel side is 25m but i drew a dotted line down and that s 20m
how do i figure the area?
thanks Answered by Penny Nom. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

From Vicki: I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





What is the height of the triangle? 
20120112 

From Hailey: The area of a triangle is 77ft2. if the base is 11ft. how tall is the height? Answered by Penny Nom. 





The dimensions of a rectangle 
20120106 

From joseph: The perimeter of a rectangle is 72 inches. The length of the rectangle
is three more than 2 times the width of the rectangle. What is the
length of the rectangle? Write and solve an equation to determine the
dimension of the rectangle. Answered by Penny Nom. 





Triangles, area and perimeter 
20120101 

From Panny: I saw a question asked on your board without an answer.
How do I find the area of a triangle any triangle if I only know the perimeter.. Answered by Penny Nom. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? Answered by Penny Nom. 





Jennifer wants to fence in her backyard 
20111209 

From Val: Jennifer wants to fence in her backyard. A yard is rectangular and is 15 feet by 12 feet. One 12foot side is against the house so it does not need fencing. How many feet of fencing does Jennifer need? Answered by Penny Nom. 





Squares and triangles 
20111206 

From Liaqath: You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Answered by Penny Nom. 





Solve for theta if 8cos^2 theta3=1 
20111202 

From Katherine: Hi,
I have just learned to solve trigonometric problems for theta and have one specific question in order to find the solutions to my homework.
I will use one example for this question. If I have 8cos^2 theta3=1
I first divide by 8 and get cos^2theta=3/8
then I have cos theta= plus or minus the square root of 3/8
Then I assume that I plug in inverse cos (the square root of 3/8) to my calculator.
How do I find the four solutions (we are typically supposed to find four, I believe?)
Can you help me with finding the solution to this problem? Thank you! Answered by Penny Nom. 





A triangle problem 
20111120 

From May: In triangle ABC, AB=AC, angle A=20,
D lie on AB making DC=AD,
E lie on AC making angle EBC=70.
Find angle DEB. Answered by Chris Fisher. 





The 3, 4, 5 right triangle 
20111115 

From rishil: to the nearest degree,what is the measure of the smalles angle in a rightt triangle with sides of length 3,4 and 5? Answered by Penny Nom. 





A right angled triangle 
20111031 

From bijo: how can i find the tangent point at a circle with origin as center with radius r and the tangent pass through a given point P? I also want to find out the third point of a right angled triangle given other two points? Answered by Chris Fisher. 





The area of a triangular garden 
20111031 

From tasha: a garden has sides of 6m,8m and 10m find the area Answered by Chris Fisher. 





Building a custom range hood 
20111008 

From Bill: I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston. 





A rectangle of largest possible area 
20110916 

From mary: Steven has 100 feet of fencing and wants to build a fence in a shape of a rectangle to enclose the largest possible area what should be the dimensions of the rectangle Answered by Penny Nom. 





A rectangle is inscribed in a circle 
20110717 

From Alexea: A rectangle is inscribed in a circle of diameter 15in. Express the perimeter as a function of the width x. Answered by Penny Nom. 





Construct a 30 degree angle 
20110610 

From Ella: they give you a simple straight line and ask you to construct an angle of 30 degrees at one end of the line using only a ruler and a compass? Answered by Penny Nom. 





What is the angle of decent? 
20110520 

From Taten: So you have an airplane with an altitude of 5.8KM. It has 46KM till the run way. What is the angle of decent? Answered by Penny Nom. 





The dimensions of a rectangle 
20110508 

From yolanda: If the length of a rectangle is 3ft less than twice its width and the area of the rectangle is 54ft^2,what are the dimensions of the rectangle? Answered by Penny Nom. 





The volume of a triangular shaped aquarium 
20110507 

From Jeff: HI, I searched the site but really couldn't find my answer,
at least that I could understand! I have a triangular shaped aquarium
( think of a cube, except its an equal triangle shape). all 3 sides are 48 inches,
and it is 34" tall. Can you please tell me what the volume is in gallons?
Thanks! Answered by Penny Nom. 





A circle inscribed in a triangle 
20110507 

From Aishwarya: The angles of a triangle are 50, 60, and 70 degrees, and a circle is touches the sides at A, B, C. Calculate the angles of the triangle ABC. Answered by Penny Nom. 





An exclusion zone around a triangle II 
20110503 

From Aishwarya: A long time ago Mr gibson found an island shaped as a triangle with three straight shores of length 3km, 4km and 5km. He declared an exclusion zone around his island and forbade anyone to come within 1km of his shore. What was the area of his exclusion zone?
This question was answered but did not understand the explanation. Answered by Robert Dawson. 





The area of a rectangle 
20110430 

From Hayley: A rectangles width is exactly twice its length. The area of the rectangle is 450 square feet. What are the length
and width of the rectangle? Answered by Penny Nom. 





cos(x) = 1/(square root of 2) 
20110427 

From Shelby: Find exact value of x for 1 <(or equal to) x < 2pi
a) cos(x) = 1/(square root of 2) Answered by Penny Nom. 





A right angled triangle 
20110422 

From jeremy: Solve the right triangle with the given sides and angles. a=3.0 cm and b=1.6 cm Answered by Penny Nom. 





Dividing a polygon into triangles 
20110416 

From Foxie: You have a given regular polygon with n vertices and you divide it into triangles(using the vertices of the polygon) which each share at least one side with the polygon. How many distinct ways can you divide the polygon if its vertices are numbered? For n=3 it's 1 way, for n=4 it's 2 ways for n=5 5 ways, I'm not quite sure but think that for n=6 it's 12 ways... thanks in advance! Answered by Claude Tardif. 





A concrete walk around a pool 
20110415 

From Skipper: I want to know the answer if you were to want a pool to be 20 ft by 30 ft and wanted a 5 ft border around it what would be the dimension of the whole area plus concrete walk Answered by Penny Nom. 





The perimeter of a rectangle 
20110404 

From aspen: the perimeter of a rectangle is twice the sum of its length and its width. the perimeter is 40 meters and its length is 2 meters more then twice its width. what is the length? Answered by Penny Nom. 





The rectangle is reduced to 90% of its original size 
20110331 

From stephon: A rectangle has a length of 4cm and a width of 8cm.
If this rectangle is reduced to 90% of its original size what will be the new length Answered by Penny Nom. 





sin x = 0.25 
20110329 

From Wayne: How do you solve for x in the equation sin x = 0.25
the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom. 





The interior angles of a pentagon 
20110310 

From Daima: I need help!
The interior angle of a pentagon i s5 ( I hope ) or 540 degrees.
The interior angle of a pentagon is what? Explain to me please.
Daima Answered by Penny Nom. 





Find the dimension of the original rectangle 
20110228 

From sandra: the perimeter of a rectangle is 40 cm. if the length were doubled and the width halved, the perimeter would be increased by 16cm. Find the dimension of the original rectangle Answered by Robert Dawson. 





Triangles with perimeter 16 cm 
20110222 

From Chong: How many triangles (up yo congruence) with perimeter 16 cm and whose lengths of its side are integers? Answered by Chris Fisher. 





Prove sin x = sin (pi  x) 
20110215 

From Janet: Prove sin x = sin (pi  x) Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





A cone with a specific angle 
20110201 

From John: Hi my daughter came with a seemingly easy question (which to me it was not)
How to make/calculate a cone of a specific angle from top to bottom radius. Answered by Penny Nom. 





The area of a rectangle 
20110131 

From T.S.: for which value of w does the rectangle below have an area of 864 square units if sides are width=w+15 and length=w15 Answered by Penny Nom. 





The sides of an equilateral triangle 
20110127 

From Cristal: Hello :) How can i find the sides of an equilateral triangle when only given the height 10m? Answered by Penny Nom. 





The area of isosceles triangle 
20110124 

From imraan: how to find the area of isosceles triangle by knowing only its sides Answered by Penny Nom. 





A rectangle 
20110116 

From meg: if a rectangle has a length that is 3cm less than 4 times its width and its perimeter is 19cm, what are the dimension? Answered by Penny Nom. 





The height of a lamp 
20110113 

From Dorothy: I need to find the lamp height with casting shadow (base line of triangle where a boy 1.6m tall stands 3m from base of street lamp and has a 2m shadow. In other words, think of a right angle triangle with zero height starting at left, then 2m to right stands boy (1.6m high). Angle (hypotenuse) increases up to top of street lamp with 'x' height and 3m base. Answered by Penny Nom. 





The angle between a line and a plane 
20110112 

From tom: what are the angles of the diagonal of a rectangular parallelepiped 2in by 3 in by 4 in
makes with the faces...
You know this is a problem that I can't figure out ...I don't know where
the angle and the diagonals where? can you help me with this one? Answered by Penny Nom. 





Tan(x+pi)tan(pix)=2tan(x). 
20110109 

From Steven: Verify the identity:
Tan(x+pi)tan(pix)=2tan(x) Answered by Penny Nom. 





The third side of a triangle 
20101228 

From andrea: in triangle abc, ab=5 and the area is 50cm2.If angle c 90degrees, find the length
of c. Answered by Penny Nom. 





Draw a figure with 16 triangles using only 6 line segements 
20101216 

From Jill: How can you draw a figure with 16 triangles using only 6 line segements? Answered by Stephen La Rocque. 





Angle of elevation 
20101210 

From PANKAJ: angle of elevation of the sun perpendicular72 and base 88 find angle Answered by Penny Nom. 





A television camera at a basketball court 
20101206 

From ryan: Can you just please give me an idea on how the diagram would look like. I'm really confused.
A television camera is 30 ft. from the sideline of a basketball court 94 ft long. The camera is located 7 ft from the midcourt. Through what angle must it sweep in order to cover all action on the court? Answered by Penny Nom. 





Can determine if it is scalene, isosceles, or equilateral 
20101201 

From Jessie: find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(3,2) P(2,1) L(2,3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this? Answered by Penny Nom. 





A rectangular piece of plywood 
20101130 

From Austin: A rectangular piece of plywood is trimmed to make it square by cutting a 4cm strip off the top and a 2cm strip off one side. If the area of the original piece is 74cm2 greater than the area of the square, find the dimensions of the rectangle. Answered by Penny Nom. 





The perimeter of a rectangle 
20101124 

From shericka: a rectangle has a perimeter of 60cm. its length is 5 times greater than its width. what is its length? Answered by Penny Nom. 





The area of an equilateral triangle 
20101111 

From ginny: If a equilateral triangle has side lengths of 41.33m how would i calculate the area?
if i don't know the height of the triangle?
thank you. Answered by Penny Nom. 





The base of an isosceles triangle 
20101024 

From Brian: how can I find the base of an isosceles triangle from the height and the perimeter? Answered by Penny Nom. 





A rectangle with rounded corners 
20101021 

From Connie: How do you find surface area if the rectangle is 100ft. by 200ft. with quarter circles in the corners with a radius of 20ft. ? Answered by Penny Nom. 





The angles in an mgon and genrealizations 
20101016 

From Michael: Hello:
In answer to a student's question, someone named Penny from
your organization provided a proof that the sum of the interior
angles of a triangle in the plane is pi radians (or 180 degrees).
I am interested (and I'm sure many other people would be too) in
3 potential generalizations of this basic fact in plane geometry: Answered by Walter Whiteley. 





The third vertex of a triangle 
20100923 

From nikos: Hi, I would really appreciate any help in this:
"Suppose you have a triangle (any triangle, no hypotheses allowed), let's call it ABC.
You know the coordinates of the two vertexes, A(x1,y1), B(x2,y2) and the area of the triagnle, let's call it D.
Can you find the third vertex of this triangle based on these facts?"
Thanks a lot! Answered by Harley Weston. 





Limiting Cases in Geometry 
20100922 

From Niki: Consider a rectangle inscribed in a circle with a radius or R. What are the possible perimeters for the rectangle? Answered by Stephen La Rocque. 





A building and a flag pole 
20100909 

From paul: A flag pole and a building stand on the same horizontal level. From the point p at the bottom of the building,the angle of elevation of the top t of the flag pole is 65 degrees. From the top q of the building the angle of elevation of the point t is 25 degrees.If the building is20 meters high. Calculate the distance pt Answered by Penny Nom. 





The height of a triangle 
20100805 

From Ann: The height of a triangle is 4cm less than the base. The area is 198cm^2. Find the height. Answered by Stephen La Rocque. 





A spaceship playhouse 
20100726 

From Dave: I would like to build a spaceship playhouse for my grandson I want it to
be about 36" around and I want to use 5/4 decking boards that measure
5 1/2" wide how do I figure out how to lay out a base pattern to nail to
(what angle do I need to cut and how many boards will it take to go around
the circle. Answered by Penny Nom. 





An octagon shaped bench 
20100709 

From rob: i am trying to build a octagon shaped bench to fit inside a 69 inch round hot tub so that the tip of each point touches the edge of the circle where it will be fastened. Answered by Stephen La Rocque. 





Rays and angles 
20100624 

From cristina: what is the formula for finding the number of angels that can be named by a given number of rays with the same endpoint? Answered by Robert Dawson. 





The height of a triangle 
20100621 

From Taylor: how do i find the height of a triangle with a base of 3 and a side of 5 the book says 4 but i cant get that Answered by Penny Nom. 





How wide a strip has he cut when the lawn is half mowed? 
20100524 

From Arib: rectangular lawn has length 40 m and width 30 m. David starts cutting from the outside in. How wide a strip has he cut when the lawn is half mowed? Answered by Penny Nom. 





The area of a triangle 
20100522 

From jose: haw many square feet are in a triangle 30 feet high with a 100 ft base? Answered by Tyler Wood. 





The area of a triangle 
20100510 

From Saeed: Show that:
Area of triangle = half of the perimeter of the triangle times
the radius of the inscribed circle !!!!!!!!!!!!!!! Answered by Penny Nom. 





The altitude of a triangle 
20100508 

From kylie: the vertex angle of an isosceles triangle is 57 degrees 24 minutes and each of its equal sides is 375.5 feet long. find the altitude of the triangle Answered by Penny Nom. 





An angle in a triangle 
20100506 

From Morgan: Question from Morgan, a student:
t
8 t t 8
t 78 t
t t
t t
t x t
ttttttttttttttttttttttttt
10
I'm having trouble solving for x I'm not sure where to start ( the ones in the middle of the triangle are both degrees) thanks in advance for your help i really do appreciate it Answered by Penny Nom. 





A wishing well 
20100504 

From Cassie: I'm trying to construct a Wishing Well made of treated 2x4 wood, so the actual measurement is 3 1/2 by 1 1/2. The well is going to be three feet in diameter. I'm trying to construct this as circular as possible, what angle should the wood panels be cut at? Answered by Penny Nom. 





A trig equation 
20100428 

From Steve: 2cos^2(X)2sin^2(x)+1=0 Answered by Harley Weston. 





cos(x) = sin(x  1) 
20100428 

From alex: In the equation cos x = sin x1 for pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
Alex Answered by Penny Nom. 





The height of a flag shaft 
20100425 

From Sarah: A man standing 20metres away from a tower observes the angles of elevation to the top and bottom of a flag shaft standing on the tower as 62degrees and 60degrees respectively. Calculate the height of the flag shaft.' Answered by Penny Nom. 





A rectangle problem 
20100412 

From Charlene: The ratio of the width to the length of a certain rectangle is equal to the ratio of its length to the difference between its length and twice its width. If the area of the rectangle is 25cm^2, then what are its dimensions? Present a non algebraic solution? Answered by Tyler Wood. 





The perimeter of a rectangle 
20100412 

From Charlene: The area of a rectangle is 390m^2. If its length is increased by 10m and its width is decreased by 6m, then its area does not change. Find the perimeter of the original rectangle. Answered by Tyler Wood. 





A regular hexagon and an equilateral triangle in a circle 
20100405 

From Beth: A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 10cm. What is the difference between the area of the hexagon and the area of the triangle? Answered by Chris Fisher. 





The diagonals of a rectangle 
20100330 

From Tabatha: The diagonals of a rectangle are 8 units long and intersect at a 60 degree angle. Find the dimensions of the rectangle. Answered by Penny Nom. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





The angle of intersection between two lines 
20100325 

From Madhumitha: How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it? Answered by Chris Fisher. 





A rectangle inscribed in a circle 
20100324 

From sadiq: here is the question,
in my mathematics book there is equation of the area of the rectangle
inscribed in a circle having equation x^2+y^2=a^2
and the area of rectangle is 4xy=4x(a^2b^2)^1/2
i don't know what is b but a is surely the radius
(i want the derivation for the area of rectangle). Answered by Harley Weston. 





A quadrilateral with 4 known sides and 1 known angle 
20100319 

From samuel: Name: Samuel
Status: Student
I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.
By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).
However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).
Is there any simpler way? Answered by Robert Dawson and Harley Weston. 





The perimeter of a rectangle 
20100312 

From makiah: A rectangle has a perimeter of 12 meters.If each side is a whole number of meters,
what are the possible dimensions for the length and width? Answered by Penny Nom. 





An irregular octagon 
20100309 

From Gayle: Question from Gayle:
I am building an irregular shaped octagon wooden box.
The measurements are 291/2 inches by 211/2 inches.
Sides are 12 inches.
It will be 36 inches high.
What would the cutting angles degrees be? Answered by Harley Weston. 





The dimensions of a rectangle 
20100303 

From Kirsten: A rectangle is twice as long as it is wide. Its area is 128 square meters. What are the dimensions of the rectangle? Answered by Tyler Wood. 





The hypotenuse 
20100227 

From Dannielle: how do you find the hypotenuse if a=8 and b=6? Answered by Penny Nom. 





How many triangles...? 
20100222 

From deciree: Given 12 points, no 3 of them on a line with 6 red, 4 blue and 2 green points.
a) How many triangles have vertices all the same color?
b)How many triangles have vertices with each vertex a different color?
c)How many triangles have at least one green vertex?
thanks to lorraine! Answered by Penny Nom. 





Triangles 
20100219 

From Wiliam: A box contains one 2 inch rod, one 3 inch rod, one 4 inch, and one 5 inch rod.
What is the maximum number of different triangles that can be made using these rods as sides? Answered by Penny Nom. 





The vertices of an equilateral triangle 
20100219 

From Emma: If two of the vertices of an equilateral triangle are (2,1) and (6,5), what
are the two possible coordinates of the third side of the triangle? Answer
in radical form. Answered by Tyler Wood. 





An isosceles triangle 
20100211 

From Kim: I am given the length of the two legs of an isosceles triangle (8), and the base angles are 30 degrees...I am asked to find the area of the triangle with only this information Answered by Tyler Wood. 





The angle at which the road is inclined 
20100210 

From abeth: a mountain road drops 5 m for every 22 m of road. Calculate the angle at which the road is inclined to the horizontal to the nearest degree. Answered by Penny Nom. 





The other two sides of a right angle triangle 
20100209 

From ayesha: how to find the other two sides of right angle triangle when length of one side and angle of other side is given i.e 45 Answered by Penny Nom. 





A dirt berm 
20100205 

From casey: My question is two fold. I want to build a dirt berm that is 95 feet long and 8 feet high which has a 45 degree angle on each side of the slope. My first question is how wide will the berm end up being? Second question is how many cubic yards of dirt will I need to get? Thanks! Answered by Harley Weston. 





Fencing a garden 
20100204 

From kris: How many meters of fencing do i need to enclose a garden if the yard is 26 meters long and half as wide? Answered by Penny Nom. 





An impossible isosceles triangle 
20100131 

From Hailey: An isosceles triangle has one angle that measures 50 degrees and another that measures 70 degrees. Why can't this triangle be drawn? Answered by Penny Nom. 





An isosceles triangle 
20100128 

From Jazzy: An isosceles triangle is a 2 congruent (equal) sides. Of the third side is three times the length of the congruent side(s), and the perimeter is 75 cm, find the length of all three sides of the triangle Answered by Penny Nom. 





The perimeter of a rectangle 
20100127 

From debbie: how many dimensions are there to get a perimeter of 400 feet for a rectangle? Answered by Penny Nom. 





A triangle in a rectangle 
20100125 

From Sangya: The perimeter of the rectangle is 21 inches. The perimeter of the inscribed triangle is 21 inches. Find the dimensions of the rectangle Answered by Robert Dawson. 





Solving a triangle 
20100125 

From Paige: how do i solve a triangle with one angle of 73 degrees,
one angle of 32 degrees, and one side of 23cm? Answered by Harley Weston. 





An altitude of the triangle intersect a side of the triangle 
20100123 

From Sarah: In what type of triangle does an altitude of the triangle intersect a side of
the triangle at its midpoint??
Sarah Answered by Walter Whiteley. 





Angle of incline 
20100120 

From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom. 





Trigonometry and picture hanging 
20100113 

From george: The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed? Answered by Penny Nom. 





The triangle inequality 
20100111 

From Nazrul: If A and B are any two vectors, then how can I prove that magnitude of (A+B)<=magnitude of A+magnitude of B. Please show me the process in details. Thank you. Answered by Robert Dawson. 





The maximum area of a rectangle 
20100103 

From Mohammad: determine the maximum area of a rectangle with each perimeter to one decimal place?
a)100 cm b)72 m c)169 km d)143 mm Answered by Penny Nom. 





Write a function for the area in terms of x 
20100101 

From Almarie: Lauren has 40 feet of metal fencing material to fence three sides of a rectangular garden. A tall wooden fence serves as her fourth side. Write a function for the area of the garden A in terms of x, the width in feet. Answered by Penny Nom. 





Triangles on a base of 2.4 meters 
20091226 

From Allan: Please,How do I calculate the height of a triangle when I only know the width of the base line,It is 2.4 mtrs. Thankyou very much. Answered by Penny Nom. 





A triangle with two equal medians 
20091219 

From Nazrul: If two medians of a triangle are equal , how can I prove that the triangle is isosceles. Answered by Chris Fisher. 





Houses on a triangular field 
20091218 

From Beth: Hi, this is the question i have to answer.
Planning permission has been granted to build houses on the triangular field in the diagram. The housing density permitted is 1 house for each 200m². Calculate how many houses can be built on this
Beth Answered by Robert Dawson. 





Polygons, diagonals and the sum of the measures of the angles 
20091218 

From jason: find the set of polygons in which the number of diagonals is greater than the sum of the measures of the angles Answered by Robert Dawson. 





The acute angle formed by intersecting lines 
20091217 

From Katie: To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x  2y = 2. Was is necessary to find the intersection point? Answered by Robert Dawson. 





An equilateral triangle is inscribed in a circle 
20091206 

From anna: An equilateral triangle is inscribed in a circle of radius 6. Find x and the length of
one side of the equilateral triangle. The picture is a triangle where the corners touch the
sides of a circle and there is a line drawn down the middle of the triangle. A point labeled
D which is in the triangle but im pretty sure that its marking the radius of the circle.
From that point D is a line going from that point to the bottom left corner of the triangle.
So this line shall make another mini triangle. The bottom of the big triangle is then split
into 2 segments and the left segment is labeled x. Please help for I am stuck! Answered by Penny Nom. 





The height of an isosceles triangle 
20091206 

From Carl: What is the height of an isosceles triangle if its base is 12cm, and its base angle is 72degrees? Answered by Penny Nom. 





The dimensions of a rectangular room 
20091126 

From crystal: . The length of a rectangular room is 7 feet longer than its width. The area of the room is 60 feet. What are the dimensions of the room? Answered by Penny Nom. 





The triangle formed by the tangent and the coordinates axes 
20091123 

From Nirmala: Given that y=1/x, x is not equal to zero. Prove that the area of the triangle formed by the tangent and the coordinates axes is 2. Answered by Harley Weston. 





The three medians of a triangle 
20091118 

From Nazrul: If the three medians of a triangle are equal, how can I prove (without using the property that the three medians of a triangle cut one another at a point of trisection) that the triangle is equilateral. Answered by Chris Fisher. 





The base and height of a triangle are in the ratio of 3:2 
20091118 

From Mike: Find the base and height of a triangle using the ratio 3:2 and an area of 108 inches square. Is there a formula we need to use?
Thanks
Mike Answered by Penny Nom. 





Three angles and one side of a triangle 
20091116 

From Esther: How do i find the sides of an acute triangle if i know the angels are 60,45,75 and i only know one side which is 10? Thanks! Answered by Penny Nom. 





The line through D(4, 0) and E(2, 6) 
20091116 

From Rogerson: The point F is on the line through D(4, 0) and E(2, 6) so that DF=4DE. Find the coordinates of F. Answered by Penny Nom. 





The fourth vertex of a rectangle 
20091111 

From Ellena: The points A(2,1), B(5,3), and C(7,0) are the three vertices of a rectangle. Determine he coordinates of the fourth vertex. Answered by Penny Nom. 





sinA + cosA = 1 
20091106 

From Nazrul: What is the solution of sinA+cosA=1 where A is an acute angle? Will A=0 degree be included in the solution? Please explain. Answered by Harley Weston. 





Is it a rectangle? 
20091029 

From sefora: The coordinates of the vertices of quadrilaterals are given.
Draw each quadrilateral on a grid.
Determine whether it is a rectangle (show your work)
P(5,1), Q(4,4), R(6,2), S(3,5) Answered by Penny Nom. 





A triangle problem 
20091028 

From Nazrul: ABC is a triangle , D is the mid point of AB and DE is parallel to BC where E lies on AC. How can I prove that E is the mid point of AC. Answered by Penny Nom. 





Cutting a pipe at an arbitrary angle 
20091024 

From Carol: I have read your article on cutting pipe,etc. at a 45 degree angle. I need to develop
an equation and pattern for cutting any size pipe (3" to 7") to any degree. I don't
understand how to transfer the wave pattern to graph paper.
Thanks. Answered by Harley Weston. 





The hypotenuse of a right triangle 
20091018 

From steven: the perimeter of a right triangle is 20 cm. its area is 15 sq cm. find its hypotenuse. Answered by Penny Nom. 





The three angles of a triangle 
20091013 

From Michelle: The second angle of a triangular garden is four times as large as the first.
The third angle is 45 less than the sum of the other two angles.
Find the measure of the other two angles? Answered by Penny Nom. 





The radius of an arc 
20091013 

From AYMAN: Question from ayman:
i would like to know the radius of an arc , i do not know the angle , can u please explian it with an example ,
all i know , or i think i know is a draw line , the reason i asked yu guys this Q , is i am a boilermaker apprentice , sometimes i do deal with a bended pipes or flate plates of metal .
when i try to do the same bend as these pipes , it is quite hard so for me to find out the radius of the pipe already bended & find out the angle i will be able to know the full length of the material thats all , thank you Answered by Robert Dawson. 





A right triangle 
20091012 

From Josseph: A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides? Answered by Penny Nom. 





The area of a rectangle 
20091010 

From Ann: given a rectangle with sides a and 2a and diagonal d, find the area of the rectangle as a function of the diagonal,d Answered by Penny Nom. 





Two rectangles 
20091008 

From Lillian: A rectangle is 5cm longer than twice its width.
The width of another rectangle is 3cm less
than the width of the first rectangle and its length is 6cm more than 3 times its
width. If the perimeters are equal, find the dimensions of both rectangles Answered by Penny Nom. 





The maximum number of right angles in a polygon 
20091005 

From Bruce: Is there way other than by trial and error drawing to determine the maximum number of right angles in a polygon? Secondary question would be maximum number of right angles in a CONVEX polygon. Is there a mathematical way to look at this for both convex and concave polygons? Or are we limited to trial and error drawing? Answered by Chris Fisher. 





A rightangled triangle 
20091002 

From Hunter: The three sides of a rightangled triangle measure x1, x+6, and 2x+1 in length.
What are the possible lengths of the hypotenuse? Answered by Penny Nom and Melanie Tyrer. 





A triangle on a sphere 
20090907 

From Rohit: How do I find the angles of a triangle drawn on a sphere (spherical triangle)? Answered by Chris Fisher. 





Is 100 degree angle an acute angle? 
20090902 

From Nazrul: Is 100 degree angle an acute angle? Please explain. Here 100<90. Answered by Robert Dawson. 





Zero Angle 
20090901 

From Nazrul: Is zero degree an acute angle? Please explain. Answered by Janice Cotcher. 





The area of a rectangle 
20090821 

From roxanne: the dimensions of the rectangle: 3x length and 4x width. What is the area of the rectangle in square units? Answered by Penny Nom. 





A paper towel roll 
20090819 

From Jeff: I am making a spiral tube with paper that is 2" in dia. and 102" long
I will be using paper that is slit 3" wide how many lineal feet of paper will
I need to to cover the 102"
I will be using 3 rolls of paper that will over lap the other by half to make
a hard tube (paper core) in a roll of paper towels
Thanks Jeff Answered by Penny Nom. 





Find the central angle 
20090818 

From Larissa: In a circle, the length of a chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle theta, in radians, correct to four decimal places. Then give the answer to the nearest degree. I think I'm supposed to use Newton's method, but am not sure how to start with this problem. Answered by Harley Weston. 





Solve for s 
20090812 

From Michelle: My daughter and I are having trouble with this problem...All it says i solve thr formula for the indicated variable.
Height of an Equilateral Triangle.
Solve for s:
H= square root of 3/2 * S Answered by Penny Nom. 





An isosceles triangle 
20090809 

From Megan: Find the perimeter of an isosceles triangle with a verticle angle of 100 degrees and a base of 25 cm.
I think I could answer this if I knew what a verticle angle was.
Thanks Answered by Stephen La Rocque. 





Eye Height Level Found from Visual Angle 
20090807 

From Jolie: Hello,
I am trying to figure out what height from the ground a person's eyes are if they have a 12 degree visual angle to a screen that is 58cm away from their eyes?
Thank you. Answered by Janice Cotcher. 





Constructing an isosceles triangle 
20090727 

From Sanjay: How to construct an isosceles triangle ABC with a base BC = 5.4 centimetre and altitude AD = 4.7 centimetre? Please help. Answered by Janice Cotcher. 





How can I trisect an angle? 
20090727 

From Nazrul: How can I trisect an angle? Answered by Robert Dawson. 





Finding Supplementary Angles 
20090724 

From emir:
Answered by Robert J. Dawson. 





The sides of a triangle 
20090708 

From Susan: The second side of a triangle is 5ft more than the length of the first side. The third side of the triangle is 10ft less than the length of the first side.
The perimeter of the triangle is 61ft. Find the lengths of each side of the triangle.
Thank you so much! Answered by Penny Nom. 





The area of a triangle 
20090702 

From Rory: I'm trying to find the area of a triangle with points 2, 1; 4,1 and 7,4 Answered by Penny Nom. 





A diagonal of a rectangle 
20090701 

From Ruben: Please assist me with the following problem: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? Thanks Answered by Harley Weston. 





Finding an Acute Angle using Trigonometric Identities 
20090629 

From Nazrul: How can I find the value of A if sinAcosA=1 , where A is an acute angle. Answered by Stephen La Rocque. 





Two questions from math class 
20090618 

From Con: Hello,
My name is Con and my son is required to answer the following questions for his maths class.
He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct?
He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution?
Q1.
Digits 2, 3, 4, 5 and 7 are each used once to compose a 5digit number abcde such that 4 divides a 3digit number abc, 5 divides a 3digit number bcd and 3 divides a 3digit number cde. Find the 5digit number abcde.
Q2.
Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD.
Con Answered by Chris Fisher. 





Stones around a pool 
20090601 

From Jessica: I am putting a yard pond in and I am trying to find out how many stones I would need for the perimeter.
The pond is 4ft (W) by ft (L) by 1.5ft (D)
Thank You,
Jessica Answered by Penny Nom. 





The dimensions of a rectangle 
20090530 

From Linda: A rectangle has a perimeter of 38 feet & an area of 48 square feet. What are the dimensions of the rectangle? Answered by Stephen La Rocque. 





I'm building a fence at my house. 
20090524 

From dylan: I'm building a fence at my house. If my hypotenuse is 50ft, what are the lengths of my other two legs? Answered by Penny Nom. 





The position of the fulcrum 
20090523 

From jim: I think I need a formula. I need to know how far an object will be lifted.
A beam is 246 inches long on one side of the fulcrum, and 41 inches on the other side,
if I push down 36 inches on the long side of the beam, how much will the short side move up? Answered by Stephen La Rocque. 





Application of Derivatives of Trig Functions 
20090521 

From Alannah: I have a word problem from my Calculus textbook that I can't figure out.
Triangle ABC is inscribed in a semicircle with diameter BC=10cm. Find the value of angle B that produces the triangle of maximum area.
I am supposed to set up an equation for the area of the triangle A=b x h/2 using Trig functions based on angle B to represent the base and height but I'm not sure how to do this when the side length given is not the hypotenuse. Answered by Janice Cotcher. 





The width of a rectangle 
20090519 

From Stacey: If the length of rectangle is fixed at 29 cm, what widths will make the perimeter greater than 82 cm? Answered by Penny Nom. 





The sum of the angles of a triangle 
20090518 

From mary: prove that the sum of the three angles inside any triangle always add up to 180 degrees? Answered by Harley Weston. 





Angles in a triangle 
20090516 

From Robert: The second angle of a triangle is twice the sizee of the first angle, the third angle is 48 degrees less than the sum of the other two angles. What are the measurements of all 3 angles?
PS: please help Answered by Stephen La Rocque. 





Finding Height of a Triangle Given Area and Base 
20090514 

From theodore: area of a triangle is 40 in ^2 and base is 4 in what is the height Answered by Robert Dawson. 





The hypotenuse of a right angled triangle 
20090511 

From Deb: Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. I've ended up with the hypotenuse = x+9, another side = x and the other side = x+7. what do i do next? Answered by Penny Nom. 





A hexagon inside a triangle 
20090503 

From Brian: How do you figure out the area of an equilateral triangle with only the clue of a regular hexagon perfectly inside it (no boarders) and the only thing you know about the hexagon is it has an area of 12cm^2? Answered by Stephen La Rocque. 





A maxmin problem 
20090420 

From Charlene: A fixed circle lies in the plane. A triangle is drawn
inside the circle with all three vertices on the circle and two of the vertices at the
ends of a diameter. Where should the third vertex lie to maximize the perimeter
of the triangle? Answered by Penny Nom. 





The interior angles of a pentagon 
20090420 

From Mary: If four interior angles of a fivesided figure pentagon measure 100 degrees each, what will the fifth angle measure? Answered by Harley Weston. 





Two similar rectangles 
20090419 

From Alyssa: The ratio of the lengths of corresponding sides of two similar rectangles is 3:5. the small rectangle has an area of 36 square centimeters. What is the are of the large rectangle? Answered by Penny Nom. 





The height of a right triangle 
20090417 

From drakkar: how do i find the height of a right triangle that in 176 feet in area Answered by Penny Nom. 





The central angle of a chord 
20090406 

From Dale: How do I find the central angle if I only have the cord length and radius. Answered by Harley Weston. 





An isosceles triangle 
20090326 

From sela: An isosceles triangle has two equal sides of length 10 cm. Theta is the
angle between two equal sides.
a) Express area of a triangle as a function of theta
b) If theta is increasing at a rate of 10 degrees/minute, how fast is area
changing at the instant theta=pi/3?
c) at what value of theta will the triangle have the maximum area?
Answered by Penny Nom. 





Depth to height ratio 
20090326 

From Janet: Is there a formula to determine how deep something (a cabinet) should be based on how tall it is? Answered by Robert Dawson. 





The base of a triangle 
20090325 

From yinna: how do I find the base of a triangle who's height is 2 times the base and the area is 9? Answered by Penny Nom. 





A 1.5:1 rectangle 
20090323 

From melody: I have an origami model that says to use a 1.5:1 rectangle. I don't understand how to calculate the size of paper I need to use. Surely there is a formula to calculate this ratio? Thanks for your help. Answered by Penny Nom. 





The base and height of an isosceles triangle 
20090323 

From Chris: How do you find the base and height of an isosceles triangle that has 2cm legs? Answered by Harley Weston. 





The height of a triangle 
20090320 

From jon: hi,
my daughter has to find the height of a triangle her side are 174ft and
184ft and the area is11,500 ft squared.
thanks for the help
jon Answered by Penny Nom. 





The perimeter of a rectangle 
20090318 

From marylyne: the perimeter of the rectangular is 70 meters. if the width is 40% of the length, find the dimensions? Answered by Penny Nom. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





Related rates 
20090314 

From Jeevitha: The side of an equilateral triangle decreases at the rate of 2 cm/s.
At what rate is the area decreasing when the area is 100cm^2? Answered by Stephen La Rocque. 





The angles of a triangle 
20090311 

From Marissa: The angles in a triangle measure 7x1, 18x+2, and 5x+10. Determine whether the
triangle is acute, obtuse, or right. State your reasons clearly. Answered by Robert Dawson. 





A right angle 
20090309 

From bill: I am a cotractor & i am laying out some piers in an L shape i need to know how to tell if they are square one side of my L is 18 feet the other is 11 feet 6 inches what is the formula to find out what the distance from point to point should be for square . I appreciate any help u can give me thank you Answered by Penny Nom. 





The height of a right triangle 
20090308 

From Anah: Could you please tell me the formula for me to calculate the height of a triangle. I have the angles and side lengths. I am trying to calculate the height of an right triangle, the dimensions are as follows:
The Base/Hypotenuse is: 8x
Side A is 2x.
Side B is 2x. Answered by Harley Weston. 





The sides of a triangle 
20090307 

From felicia: ona map, tannersville, chadwick, and barkersvile for a triangle. Chadwick is
70 miles from Tannersville and Barkersville is 90 miles from Tannersville. Which is a
possible distance between Chadwick and Barkersville?
a. 5miles
b. 10 miles
c. 150miles
d. 200 miles Answered by Harley Weston. 





Is ACB a right angle? 
20090302 

From racheal: how to i prove angle ACB is not a rt. angle when given AT=BT=5;CT=4 in a indirect proof? Answered by Robert Dawson. 





Triangles within triangles 
20090224 

From Mari: a large shaded triangle changes each day with a white triangle appearing
in the center of each shaded one. If this pattern continues, how many white
triangles will be there on the 6th day? On the 6th day, what fraction of
the large outer triangle will be white?THANKS! Answered by Robert Dawson. 





Trig functions without geometric data 
20090224 

From bob: I do not understand how it is possible to find the sine, cosine, or tangent of an angle if
there is no hypotenuse, opposite or adjacent side?! Answered by Robert Dawson. 





Angle of depression 
20090218 

From Meeka: An aircraft flying at an altitude of 2000m is approaching an airport.
If the angle of depression of the airport is 5 degrees, what is the distance from the plane to the airport measured along the ground?
Round your answer to the nearest tenth of a kilometer. Answered by Robert Dawson. 





The height of a triangle 
20090214 

From GARIMA: IF THE SIDES OF TRIANGLE ARE GIVEN . HOW WE WILL
CALCULATE THE HEIGHT OF TRIANGLE. Answered by Penny Nom. 





Forming an arc with 2 inch steel 
20090211 

From Craige: I need to calculate the bending radius of 2" wide steel to achieve given inside and outside arc lengths Answered by Harley Weston. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





The height of a triangle 
20090206 

From lisa: find the height of a triangle, which can be split into two right triangles, but the base (4') is not split equally in half. No interior angles are given.
side a=3', side b=5' Answered by Penny Nom. 





The height of a triangle 
20090205 

From Theresa: Find the area of a triangle by first finding the height. base30ft hypotenuse50ft Answered by Penny Nom. 





A 306090 triangle 
20090203 

From Inez: If you have a 306090 triangle and the only side you get is 73 and a 90 degree box, how do you find the area? Answered by Penny Nom. 





The height of an isosceles triangle 
20090129 

From Mariah: An isosceles triangle has sides 10cm, 10 cm and the base 4cm.
How do you find out the height of the triangle? Answered by Penny Nom. 





Find area of the rectangle in terms of L. 
20090127 

From Arlen: The length of a rectangle is L. The width is 8 less than the length. Find area of the rectangle in terms of L. Answered by Penny Nom. 





The area of a triangle 
20090125 

From black: Explain how the formula for the area of a triangle can be determined by using the formula for the area of a parallelogram. Answered by Penny Nom. 





1 foot drop every 25 feet 
20090122 

From jerry: 1 foot drop every 25 feet what is the angle of the degree Answered by Penny Nom. 





The height of a triangle 
20090120 

From ELEY: WHAT IS THE HEIGHT OF A TRIANGLE IF THE AREA IS 32.4 AND A BASE OF 6.75? Answered by Robert Dawson and Penny Nom. 





A triangle with sides of length 6 and 7 
20090120 

From bill: If I have a triangle with sides 6 and 7,
which of the following is a possible area?
The answers are 13 and 21, but not 24.
I know this is because of a possible range of heights,
but how do I calculate the range of heights?
This is an SAT question. Thanks Answered by Chris Fisher. 





The area of an isosceles triangle 
20090119 

From faris: how to calculate area of isosceles triangle with two angles of 45 degree and base of 6 Answered by Penny Nom. 





The ratio of the measures of the three angles of a triangle 
20090118 

From mary: The ratio of the measures of the three angles of a triangle is 2:5:8. What is the measure of each angle of the triangle? Answered by Robert Dawson and Harley Weston. 





The dimensions of a pool 
20090118 

From denise: a rectangular swimming pool is three times as long as it is wide. if the perimeter of the pool is 320 feet, what are its dimensions Answered by Penny Nom. 





A stack of rectangles 
20090111 

From ashwani: Could you please advise the area of a rectangles pyramid.
There are 5 rectangles placed one above the other. The top most rectangle has length 2 cm and height 2 cm. The subsequent rectangles length is increased by 1 cm on both the sides, while the height of the 2nd and 3rd rectangle is 2cm each, while the 4th & 5th has a height of 3 cm each. Could you please let me know the the area of the figure and the formula to calculate Answered by Penny Nom. 





A flattopped pyramid 
20090110 

From Tom: I am planning to build an open ended, flattopped pyramid with a
rectangular base 28 x 36 in.; a square top 6 x6 in.; and a vertical
height of 16 in.
I know how to calculate the dimensions of each of the pyramid sides but
I don't know how to calculate the interior angles when I bend the sheet
metal. I will cut the four sides separately and add a one inch flange
to each "vertical" edge of the two larger sides to allow for
a bonding surface for the assembly. How do I calculate that angle? I
know it will be greater than 90 degrees but by how much? Answered by Harley Weston. 





Two angles are supplementary 
20090108 

From Stephanie: two angles are supplementary, one of the angles is 30 degrees more than double the other angle.
find the first angle, the second angle the complement of the given angle. Answered by Robert Dawson. 





Two rectangular plots have the same area 
20081223 

From Jason: Two rectangular plots have the same area. The first has a perimeter of 40m while the second has a length 2m less than the first and a width 1m greater. Find the length and breadth of the first rectangle Answered by Stephen La Rocque. 





The area of a triangle 
20081223 

From ashiya: Hi,
I have attached figure of the triangle, Can you please help to find the area of Triangle ABC.
Thanks.
Ashiya Answered by Stephen La Rocque. 





Pouring angles for a crucible 
20081220 

From Richard: I am trying to work at pouring angles and volume left in during pouring a crucible, The crucible is cylindrical and flat bottomed.
I know the diameter, radius and volume of the crucibles. and the volume of liquid going into it.
So lets say the crucible is only half full firstly I need to work out the angle just before its going to pour. ( I can work this out as long as there is a certain volume of liquid if its not enough I cant do it)
Now the problem I also need to work out how much I should tilt the crucible to allow a certain amount out and be able to do this untill the volume reaches 0 at 90' turn. This is where I am stuck.
The reason for needing to be able to work this out is so i can develop a constant flow for example 10Kg of metal per second.
Thank you very much for you time Answered by Harley Weston. 





A standard bill on a highway 
20081219 

From Stephanie: A standard bill on a highway has a perimeter of 14 feet. the length of the bill board is 6 feet greater than triple the width.
What is the length?
what is the width? Answered by Robert Dawson and Penny Nom. 





The volume of a feed hopper 
20081218 

From John: I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks. Answered by Robert Dawson. 





The angle between two lines 
20081217 

From abhi: how to calculate the angle between two lines, given the length of the lines..
angle should vary from 0  360 in the counterclockwise direction Answered by Robert Dawson and Harley Weston. 





An equilateral triangle 
20081217 

From lorraine: an equilateral triangle has side lenghts of10.the length of its altitude is? Answered by Penny. 





A rectangle with diagonal 8.5 inches 
20081214 

From nekasia: what is the area of a rectangle with a diagonal of 8.5 inches PLEASE SHOW WORK Answered by Penny Nom. 





The third vertex of a right triangle 
20081210 

From prashant: how to calculate coordinates of third vertex in a right angle triangle given the coordinates of hypotenuse as (1,3) and (4,1) Answered by Robert Dawson. 





The centroid and circumcircle of a triangle 
20081209 

From prateet: in an equilateral triangle prove that the centroid and centre of the circumcircle coincide
here i am not clear about the concept of centroid and circumcircle
i cant understand how AGis 2/3 AD.
please help in details about the topic mentioned. Answered by Harley Weston. 





The sides of a rectangle 
20081208 

From Mitchell: The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm.
The equation associated with segment AD is 3x+4y60=0
Point C is at (18, 14).
What is the length of segment AD? Answered by Penny Nom. 





The area of an isosceles triangle 
20081202 

From prateet: the area of an isosceles triangle is 60 sq cm and one of its equal sides is 13 cm. Find the base of the triangle. Answered by Penny. 





3 equidistant points 
20081201 

From Damien: How do you find 3 equidistant points (C,D,E) on a line between point A(Xa, Ya) and point B(Xb, Yb) so that AC, CD, DE and EB are all equal? Answered by Chris Fisher. 





The height, base and perimeter of a triangle 
20081117 

From Zack: How would i calculate the height of a triangle if the base is 10cm and the area is 50cm²?
If possible how would i calculate the length around the the triangle. Answered by Penny Nom. 





A triangle inscribed in a circle 
20081117 

From Wanda: I have the same question that you guys answered 20070302. I need more clarification. I UNDERSTAND how to get the radius=3, I get that it is an equilateral triangle so each vertex is 60 degrees, I get that area of triangle is 1/2 bh.
I DO NOT understand why we multiply area X 3 , or how to calculate the values of base and height. Please explain a little further. Thanks.
Wanda Answered by Penny Nom. 





The midpoint o a line segment 
20081115 

From Jane: The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





Supplementary angles 
20081110 

From Anna: <A and <B are supplementary angles. Twice the measure of <B is onefourth the measure of <A. Find the measure of both angles. Answered by Penny Nom. 





A flagpole and a yardstick 
20081107 

From Wanda: One boy holds a yardstick vertically at a point 40 feet from the base of the flagpole. The other boy backs away from the pole to a point where he sights the top of the pole over the top of the yardstick. If his position is 1 ft 9 in from the yardstick and his eye level is 2 ft above the ground, find the height of the flagpole. Answered by Penny Nom. 





The dimensions of a rectangle 
20081107 

From laela: A rectangle is 8 feet long and 6 feet wide.If the dimension is increased by the same number of feet,the area of the new rectangle formed is 32 square feet more than the area of the original rectangle.By how many feet was the each dimension increased? Answered by Penny Nom. 





The height of an equilateral triangle 
20081106 

From touqeer: My question is that how can we find the height of an equilateral triangle without using pythagoras theorem? Answered by Penny Nom. 





The angles of a triangle 
20081031 

From kyla: an isosceles triangle has two 50 degrees angles.what is the measure of the third angle? explain how you found your answer. Answered by Penny Nom. 





Three congruent rectangles 
20081027 

From Meagan: Here is my problem: Three congruent (nonsquare) rectangles are placed
to form a larger rectangle. [Two are oriented the same way and the
"stacked" while the third is rotated 90 degrees and placed next to the
other two.] The total area is 1350 square cetimeters. Square ABCD is
then created that has the same perimeter as the large rectangle that was
created. E is the midpoint of line CD and F is the midpoint of BC. Find the
area of triangle AEF. Answered by Penny Nom. 





The length of a rectangle is 6 inches less than 3 times its width. 
20081026 

From Angela: The length of a rectangle is 6 inches less than 3 times its width. Find the
dimensions of the rectangle if its area is 45 square inches. Answered by Penny Nom. 





Area of a triangle 
20081022 

From Jia: I need to find 3 ways of finding the area of a triangle. I've already had one method down which is b x h and divided by 2. What other 2 ways can i find the area of a triangle? Answered by Chris Fisher. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





The dimensions of a rectangle 
20081016 

From cristine: the area of a rectangle is 675sq.cm.
if the width is 1/3 of the length.
find the dimensions of the rectangle.... Answered by Penny Nom. 





Octagon angles 
20081006 

From John: My daughter wants to build an octagon using PVC pipe fittings. There are several pipe "elbows" available, including 45 degree. I'm trying to determine if if an octagon can be constructed by using 8 pairs of 45 degree elbows, connected to each other by 8 sections of straight pipe of some equal legnth. This makes sense to me intiutively, but I do not know how this can be properly expressed in geometric terms. Answered by Chris Fisher, Victoria West and Harley Weston. 





The height of a right triangle 
20081006 

From David: Could you please tell me the height of a right angle triangle when the base measurement is 4930mm and the base/hypotenuse angle is 10 degrees.
this will help a lot. Answered by Harley Weston. 





An arc and an angle 
20081005 

From Cory: I have a chord length of 150'. From the left starting point, I know that
30' right of starting point is 9' in height. This would be the top of the arc.
What is the arc in degrees and can anyone display an image to help me
understand? Answered by Penny Nom. 





Finding the Distance Between Two Latitudes 
20081002 

From Samua: Assuming that the Earth is a sphere of radius 4000 miles and that the cities
are on the same longitude (one city is due north to the other). Find the distance between
the cities with the latitudes of 37 degrees 47'36'' and another city with 47 degrees 37'18''. Heeeeeeeeeeelp! Answered by Janice Cotcher. 





The perimeter of a triangle 
20080929 

From Debbie: How do I calculate the perimeter of a triangle if the lengths of two sides are equal and all the angles are known? Answered by Harley Weston. 





How tall is the wall? 
20080929 

From ash: you and bob are separated by a tall wall you stand 10 feet further from the wall
than bob your angle of elevation is 37 degrees and his 44 degrees
how tall is the wall? Answered by Penny Nom. 





What is the perimeter of the rectangle? 
20080927 

From Pauline: A rectangle has an area of 27 squared inches. the height is 3 times the base
What is the perimeter of the rectangle? Answered by Penny Nom. 





The vertices of a triangle 
20080927 

From T.: how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x3y17=0,4x9y+13=0? Answered by Harley Weston. 





The base of a triangle is twice its height 
20080926 

From carolyn: The length of the base of a triangle is twice its height. If the area od the triangle is 100 square kilometers, find the height. Answered by Penny Nom. 





A right triangle 
20080925 

From john: a right triangle has hypotenuse wich measures 20cm and a perimeter 47cm. find the measure of the remaining two sides Answered by Harley Weston. 





Consecutive Even Integer Sides of a Triangle 
20080924 

From Brad: I am having a problem coming up with a formula for my son's eighth grade math problem.
We have found the answer by guess and check but have a mental block on the equation.
Any help would be appreciated.
The problem is: A right triangle has sides whose lengths in feet are consecutive even intergers. Determine the length of each side.
Thanks Answered by Janice Cotcher. 





The height and base of a triangle 
20080912 

From Bailey: The length of the base of a triangle is 1cm less than 5 times the height of the triangle. The area of the triangle is 21 square cm. What is the the height of the triangle and the length of the base of the triangle? Answered by Stephen La Rocque. 





Cutting a pipe on a 45 degree angle 
20080912 

From Bakshani: how do you a mark a pipe 5 inch diameter and cut it to form a 45 degree angel Answered by Stephen La Rocque. 





A garden in the shape of an isosceles triangle 
20080912 

From Rita: Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his garden will be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle. Answered by Penny Nom. 





The perimeter of an equilateral triangle 
20080911 

From Gerry: How can I find the perimeter (length of side) of an equilateral triangle if the only information I have is the altitude? Answered by Penny Nom. 





Supplementary angles 
20080911 

From Shanaz: Find an angle such that 3 times its supplement equals 450. Answered by Penny Nom. 





Angle of elevation 
20080909 

From kristy: A man on the tenth floor of a building shouts down to a person on the street. If the angle of elevation from the street to the man in the building is 35° and the man in the building is 40 feet up, about how far away from the building is the person on the street? Answered by Penny Nom. 





The height of a tree 
20080909 

From danice: At a certain time of day, the angle of elevation of the sun is 30°. A tree has a shadow that is 25 feet long. Find the height of the tree to the nearest foot. Answered by Penny Nom. 





The perimeter of a right triangle 
20080909 

From Shanon: I know that A=1/2bh, but for the life of me cannot figure out my 6th graders math problem.
What is the perimeter of a right triangle whose area = 600 sq. ft. Answered by Victoria West. 





Finding the Speed of a Truck 
20080908 

From Rita: A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle theta between the highway and the line of observation from the patrol car to the truck is measured.
(a) If the angle measures 15 degrees, how fast is the truck traveling? Express the answer in feet per second and miles per hour. Answered by Janice Cotcher. 





An exclusion zone around a triangle 
20080907 

From Awrongo: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Stephen La Rocque and Penny Nom. 





A security camera 
20080907 

From Rita: A security camera in a neighborhhod carnival is mounted on a wall 9 feet above the floor inside a video gallery. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall? Answered by Stephen La Rocque and Harley Weston. 





The length of an arc 
20080904 

From Angie: Segment PR is a diameter of circle S. If angle P =3D 25, find minor
arc QR.
This circle has an isosceles triangle in it, it is connected to the
diameter, Answered by Harley Weston. 





Largest Inscribed Rectangle 
20080903 

From astrogirl: find the shape and area of the largest rectangle that can be inscribed in a circle of a diameter a=2 Answered by Janice Cotcher. 





A triangle and an inscribed circle 
20080901 

From Nancy: I'm a computer programming student, and I'm supposed to figure out how to find the area of a circle inside a triangle if someone types in the length of each side of the triangle.
So, a user can type in any three numbers they want into the three "side length" boxes, and I have to find the area of the circle that would fit inside the triangle they create from those values.
So the circle can be any size, depending on the size and shape of the triangle the user creates. The circle has to touch all three sides of the triangle somewhere. Then, my program calculates the area of the triangle and thus the area of the circle. I just need to know how the circle would change depending on the length of each side of the triangle that the user puts in. Is there a way to find out how the circle's area is related to the triangle around it? Answered by Chris Fisher. 





A roof angle 
20080830 

From carla: Use vectors to find the angle in the attached diagram Answered by Chris Fisher and Stephen La Rocque. 





Number of angles formed by rays 
20080829 

From Shon: what is the formula for finding the number of angels that can be named by a given number of rays with the same endpoint? Answered by Stephen La Rocque. 





The lengths of the sides of a rectangle are in ratio 5:3 
20080829 

From todd: the lengths of the sides of a rectangle are in ratio 5:3 the perimeter of the rectangle is 32 cm find the length of each side Answered by Stephen La Rocque. 





Angles in an octagon 
20080826 

From Arvie: I have seen your answer to Kay on how she can find the length for the sides of an octagon for a 4 foot window, but what is the angle that will need to be cut to get to 4 feet Answered by Penny Nom. 





The area of a triangle 
20080825 

From Beverly: What is the area of a triangle on a graph with the following points:
18,110
6, 110
12, 100 Answered by Penny Nom. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Joining vertices in a polygon 
20080818 

From Megan: I'm trying to develop a relationship between the number of points of a regular polygon and the
(a) number of lines you could draw between those points,
(b) number of triangles you could draw,
(c) number of quadrilaterals,
etc. Answered by Penny Nom. 





Solving for Shared Height of Two Right Triangles 
20080817 

From Heidi: find the height of a triangle, which can be split into two right triangles, but the base (50m) is not split equally in half. one end of the base is 40 degrees, while the other is 30 degrees. Answered by Janice Cotcher. 





TRIG IDENTITIES 
20080817 

From VINCE: HOW DO YOU SIMPLIFY THE FOLLOWING:
2sin3(theta)cos3(theta)?
Regards Answered by Harley Weston. 





Similar Triangles Given a Median 
20080817 

From RAM: Sides AB , AC and median AD of a triangle ABC are respectively proportional to
PQ PR and median PM of another triangle PQR. Show that ABC is similar to PQR Answered by Janice Cotcher. 





Similar triangles 
20080812 

From ramarao: D is a point on side BC of a triangle ABC such that BD/CD=AB/AC. prove that AD is the bisector
AD is the bisector of BAC Answered by Chris Fisher. 





The base of a triangle 
20080810 

From Mark: What is the formula I need to use to find the base of a triangle sail that is 16 feet high and has an area of 64 square feet. Answered by Stephen La Rocque and Penny Nom. 





Angles in a regular tetrahedron 
20080807 

From Carla: Hi guys,
A regular tetrahedron has all its edges 8cm in length.
Find the angles which an edge makes with the base.
Thanks.
Carla Answered by Penny Nom. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





The angle between two faces of a pyramid 
20080806 

From Carla: A pyramid has its vertex directly above the centre of its square base.
The edges of the base are each 6cm, and the vertical height is 8cm.
Find the angle between 2 adjacent slant faces. Answered by Penny Nom. 





Some angles in a pyramid 
20080804 

From Carla: A symmetrical pyramid stands on a square base of side 8cm. The slant height of
the pyramidis 20cm. Find the angle between the slant edge and the base, and the angle between
a slant face and the base. Answered by Penny Nom. 





Area of triangle formed by three tangent circles 
20080731 

From brian: Three circles with radii 3,4 and 5 touch each other. The circles are tangent to each other. What is the area of the triangle formed by the centers of the circles? Answered by Stephen La Rocque. 





Finding Angles in a Pyramid 
20080730 

From Carla: A pyramid has its vertex directly above the centre of its square base. The edges of the base
are each 8cm, and the vertical height is 10cm. Find the angle between the slant face and the base,
and the angle between the slant edge and the base. Answered by Janice Cotcher. 





Inscribed Rectangle 
20080730 

From Felicia: A rectangle whose base is twice its altitude is inscribed in a circle whose radius is 5 mm.
Find the area of the rectangle. Answered by Penny Nom. 





An equilateral triangle 
20080721 

From Meagan: An equilateral triangle has vertices at (0,0) and (6,0) in a coordinate plane. What are the coordinates of the third vertex? You may want to sketch it out.
Note: The sides of an equilateral triangle are identical in length. Answered by Harley Weston. 





The height of a triangle 
20080718 

From Becc: I have to find the height of a triangle.
The base is 3.1cm say ab
One of the top sides is 4cm say ca
The other side is 2cmsay cb Answered by Penny Nom. 





Graphing Using Double Angle Identities 
20080716 

From Hodan: the Question is:
Describe how you could use your knowledge of Double angle formulas to sketch the graph of each function. Include a sketch with your description.A) F(x)=sin x cos x
B)F(x)=2 cos(squared)x
C) F(x)= tan(x) (divided) by 1tan(squared) x Answered by Janice Cotcher. 





An isosceles triangle inscribed in a circle 
20080715 

From Anne: Here is the math problem quoted from book:
"An isosceles triangle is inscribed in a circle of radius R,
where R is a constant. Express the area within the circle but outside
the triangle as a function of h, where h denotes the height of the triangle." Answered by Penny Nom. 





The area of a triangle  no height given 
20080712 

From phoenix: given triangle with angles 30,105 45 degrees. base = 2radical 2, no height given Answered by Penny Nom. 





Hexadecagon 
20080709 

From Dave: I would like to know at what length and angle I would cut wood to make a Hexadecagon. Answered by Penny Nom. 





Two triangles and a circle 
20080703 

From Anita: An equilateral triangle with side of length 1 cm is inscribed in a circle. A second equilateral triangle is circumscribed about the circle with all sides tangent to the circle. Find the length of a side of the second triangle. Answered by Harley Weston. 





Fit 7 different rectangles on grid paper 
20080702 

From anonomous: I need to fit 7 different rectangles on grid paper of 1cm squared.
Each squared centimetre equals 4 squared metres, and it needs to end up as area 64 square metres. Answered by Janice Cotcher. 





The exterior angles of a polygon 
20080626 

From evelina: how many sides has a regular polygon if the measures of the exterior angle is given Answered by Walter Whiteley. 





A rectangle 
20080626 

From SEBASTIAN: How to arrange quadrilateral in the form of a rectangle? Answered by Penny Nom. 





The height of an isosceles triangle 
20080622 

From Evelyn: Hi! I am facing problem finding the height of the isosceles triangle. Answered by Penny Nom. 





sin(2x)/sin(3x) 
20080619 

From matt: how does sin2x break down (not with identities) and how would sin3x be created. My
prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break
down. I want to be able to cancel out sins. Thanks! Answered by Harley Weston. 





A space camera circles the Earth 
20080616 

From Rita: A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h.
(d) If d is to be 3500 miles, how high must the camera orbit above Earth?
(e) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen? Answered by Penny Nom. 





The length and width of a rectangle 
20080611 

From gregg: the perimeter of a rectangle is 70 feet. the ratio of length to width is 4:3. how would i calculate the length of the height and width? Answered by Penny Nom. 





The angles of a parallelogram 
20080611 

From light: ABCD is a parallelogram. If angle A. = (4x=17)degrees and angle B. = (3x5)degrees , what is angle c? Answered by Penny Nom. 





What are the dimensions of the rectangle? 
20080611 

From Denise: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? Answered by Claude Tardif and Victoria West. 





The two acute angles in a right triangle 
20080605 

From Crystal: In the right triangle the ratio of the measure of the two acute angles is 4:1. What is the measure in degrees of the larger acute angle? Answered by Penny Nom. 





The interior angles of an 18sided polygon 
20080604 

From Alfred: How do I find the sum of the interior angles of an 18sided polygon? Answered by Janice Cotcher. 





The area of a rectangle 
20080527 

From Becky: the area of a rectangular lot is represented by 6t^2+13t5. What are the length and the width of the rectangular lot? Answered by Harley Weston. 





A triangle and a square 
20080524 

From s: how to construct a triangle whose area is equal to the area of a given square? Answered by Penny Nom. 





What is the length of the 3rd side? 
20080523 

From lee: If you have a triangle 12ft across the bottom then on the right is a 90 degree
angle and that side is 18ft tall. What is the length of the 3rd side? Answered by Penny Nom. 





The angles of an irregular pentagon 
20080520 

From victoria: The sum of the measure of two angles is 240. If the remaining angles are congruent, what is the measure of each angle? Answered by Penny Nom. 





A triangle inscribed in a semicircle 
20080519 

From Larissa: Find the area of the shaded region outside of a triangle inscribed (meaning the all three points of the triangle are on the circle ) in a half circle of diameter 10 inches, if one side of the triangle is the diameter and the other side is 8 inches long. (A triangle that is inscribed in a triangle is a right triangle by definition.) Answered by Penny Nom. 





The wedges in a circle graph 
20080518 

From Libby: I don't understand how to do this word problem:
The cafeteria workers distributed a survey to the student body asking students to pick 1 from a list of 5 choices for their favorite lunch. The circle graph below gives the results of the survey for the students who responded. What is the measure, in degrees, of the central angle for each choice?
And there is a pie chart that has food choices with these percentages: 25%, 20%, 15%, 10%, and 30% Answered by Leeanne Boehm and Penny Nom. 





A right angled triangle 
20080516 

From bryan: The sides of a right angled triangle are x, x+1, x+2 cm. Find the perimeter. Answered by Penny Nom. 





The sides of a rectangle 
20080516 

From bill: The area of the rectangle is 170 sq.ft. the width is unknown and the length is the width plus 7 ft.
I set it up like this w(w+7)=170 and this is where I get lost. Thanks, Bill Answered by Penny Nom. 





Fencing around a playground 
20080515 

From Vanessa: If the playground is a rectangle with it's width 10ft shorter than it's length,
and it can be enclosed by exactly 140ft of fence,
what is the length and width of the playground? Answered by Penny Nom. 





An isosceles triangle 
20080507 

From Jay: Given: An Isosceles Triangle with the area=16m squared. What would be the length of each leg. Answered by Stephen La Rocque. 





Fencing a triangular field 
20080429 

From Julieta: The area of a field shaped like a triangle is 750yards squared. One leg of the field is fenced with wood costing $5/yd. The remainder of the perimeter of the field is fenced with steel costing $10/yd. The perimeter of the field is 150yards. the total cost of the fencing is $1200.
a. What is the length of the leg fenced with wood?
b. what is the length of the leg fenced with steel? Answered by Penny Nom. 





The Pythagorean theorem with triangles rather than squares 
20080429 

From Zachary: I need to figure out how to prove the pythagorean theoorem using equilateral triangles
instead of using square. I know that A^2+B^2=C^2, but how do you get that by using equilateral
triangles. I know the area of a triangle is BH1/2=Area. So what i need to know is how to derieve the
formula of a triangle to get the pythagorean theorem Answered by Penny Nom. 





A rectangle inscribed in a circle 
20080427 

From sridhar: A rectangle with perimeter 28 cm inscribed in a circle of radius 5 cm
find the area ? Answered by Penny Nom. 





A circle inscribed in a triangle 
20080426 

From Amar: I have been given a circle inscribed in a triangle and have been told to prove that the ratio of the perimeter of the triangle to the circumference of the circle is the same as the ratio of the area of the triangle to the area of the circle. How would this be done? Answered by Stephen La Rocque and Walter Whiteley. 





Find the length and the width of the rectangle 
20080424 

From Vickie: A rectangle is 2 times longer than it is wide. It has a diagonal length of 50 centimeters. Find the length and the width of the rectangle. Round your answers to the nearest tenth. Show your work. Answered by Penny Nom. 





The dimensions of a rectangle 
20080420 

From Brandy: Find the dimensions of a rectangle with a primeter of 54 cm if the length is 5 less than three times the width. Answered by Penny Nom. 





The height of a triangle 
20080417 

From Trent: I need to know the area of a triangle. One side is 5 the base is 12 and the angle between them is 52 degrees. No height is specified. How do I find the height to get the area? Answered by Penny Nom. 





A 306090 triangle 
20080416 

From Ron: 306090 triangle. Base is 2.75 how do I find the length of the other two sides? Answered by Penny Nom. 





The three sides of a triangle 
20080416 

From Bridgett: The sum of the lengths of any 2 sides of a triangle must be greater than the third side. If the triangle has one side that is 11 CM, and the second side of the triangle is 4 cm less than twice the third side, what lengths do the 2nd and 3rd side have to be?
between 00000000 and 99999999 Answered by Stephen La Rocque. 





Chord, radius, arc length and central angle 
20080415 

From Cindy: There is a railroad curve with a chord length of 2000 ft. and a central angle of 35 degrees. What is the radius and arc length of the circular arc? Answered by Stephen La Rocque. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





An isosceles right triangl 
20080409 

From Stephanie: An isosceles right triangle has an area of 35 sq cm. What are the lengths of the sides? Answered by Walter Whiteley. 





Side lengths and angles in a regular octagon 
20080409 

From Lori: I am a builder and need to find the length of the sides of an octagon. I know the length between
the parallel sides (26 feet). What is the length of each side? What is the angle measurement? Answered by Harley Weston. 





The angle between the hands on a clock 
20080404 

From Kristin: The question I need help with is : Bobo looked at the clock at 1:25. What was the precise measure of the angle formed by the hour and minute hands of the clock? Assume that each of the clock hands moves at a constant rate continuously around the face of the clock. Thus, in any given fractional part of an hour, each hand will move that same fractional part of an hour's worth of movement. Answered by Stephen La Rocque. 





Perimeter, area and diagonals of a rectangle 
20080403 

From jenea: I have to find the perimeter as well as the area of a rectangle when given the diagonals are 12 units long and they intersect at a 60 degree angle. how do i find both the area and perimeter; do i use the 30 60 90 triangle rule? Answered by Stephen La Rocque and Penny Nom. 





The rectangle with smallest perimeter 
20080401 

From nicole: when given an area,squares are the rectangles with the smallest perimeter write the length and width of the rectangle with the smallest perimeter Answered by Penny Nom. 





A fish tank in the shape of an irregular pentagon 
20080329 

From richie: i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be
24"
24"
8"
8"
32"(approximately)
there will 3 right angles A, B, E
my question is how to figure out the degree of the angles that are not right angles (C,D)? Answered by Chris Fisher. 





The area of an equilateral triangle 
20080328 

From ElizabethMorgan: I have a problem that reads:
Find the area of a triangle with sides of 4 cm. Find the height first.
This means that I have an equilateral triangle, and I need a formula
to calculate the height using the base, and the sides. Answered by Stephen La Rocque. 





Similar triangles 
20080326 

From Nisha: In triangle ABC, LM is parallel to AB. If AL=x3,AC=2x,BM=x2,BC=2x=3. Find x Answered by Penny Nom. 





The area of a rectangle 
20080325 

From Raphael: What is the area of rectangle that measures 7 yards by 23 yards Answered by Penny Nom. 





A word problem about a triangle 
20080323 

From kathy: The measure of the largest angle of a triangle is twice the measure of the second largest. The measure of the second largest is 20 degrees more than the measure of the smallest. Find the measure of each angle. Answered by Melanie Tyrer. 





The area of the triangle with vertices (1,8), (1,1), and (5,1) 
20080323 

From jimmy: find the area of a triangle whose vertices are
(1,8), (1,1), and (5,1) Answered by Penny Nom. 





Angles subtended by the same arc 
20080323 

From Reid: Prove that two inscribed angles subtended by the same arc are equal. Answered by Stephen La Rocque. 





The area of a right triangle 
20080319 

From Tate: I need to find the area of a right triangle. I already know that the formula would be a squared + b squared = c squared. However, I only have the length of the hypotenuse and the base. Answered by Victoria West. 





The area of an equilateral triangle 
20080316 

From michael: my daughter has been given a task and I'm stuck too.
if an area of an equilateral triangle = 85cm squared
there are no other dimensions provided.
how do I calculate the length of each side ? please Answered by Penny Nom. 





The area of a triangle 
20080314 

From Tara: Area of triangle is 4,018 square yards. Its base is 82 yards. What is its height? Thanks Answered by Stephen La Rocque. 





Side lengths and area of a triangle 
20080308 

From angela: In the diagram of ABC the angle A is 65 the angle B is 70 and the side opposite vertex B is 7. Find the length of the side opposite vertex A and find the area of ABC Answered by Penny Nom. 





Two circles and a triangle 
20080307 

From Adrian: The vertices of a rightangled triangle are on a circle of radius R and the
sides of the triangle are tangent to another circle of radius r. If the lengths
of the sides about the right angle are 16 and 30, determine the value of
R+r Answered by Penny Nom. 





A fence around a rectangular region 
20080306 

From sharon: a farmer want to make a rectangular fence he has 750 feet of material . if the width is 95 feet what is the area of the rectangle Answered by Penny Nom. 





The dimensions of a rectangle 
20080306 

From Julie: Find the dimensions of a rectangle with an area of 400. Width x ft.
Length (2x7)ft. Answered by Stephen La Rocque and Penny Nom. 





Is every rectangle a square? 
20080304 

From Odette: if every square is a rectangle, is every rectangle aslo a square? Answered by Penny Nom. 





A 6 pointed star 
20080304 

From Siddharth: When 2 congruent equilateral triangles share a common center, their union can be a star
If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?
a) 60 b) 70 c) 80 d)90 e)100 Answered by Stephen La Rocque. 





The angles of a triangle 
20080301 

From Allen: How to find the other two angles of a scalene triangle if one angle is given Answered by Steve La Rocque and Penny Nom. 





Is a square a rectangle? 
20080229 

From Jaime: Is a square a rectangle? Answered by Penny Nom. 





A triangle problem 
20080228 

From Jessica: Triangle ABC Angle C is 3 times angle A angle B is 30 degrees less than angle C what are the measurements of the angles
I have the measurements and I have the Equation but I can't figure out quite how to solve it the proper way Answered by Stephen La Rocque. 





A proof in geometry 
20080227 

From Kimberly: I'm trying to write a proof for the following: If all altitudes are equal in an equilateral triangle then all sides are equal. Answered by Stephen La Rocque and Penny Nom. 





A right triangle 
20080225 

From Ali: The length of a hypotenuse of a right triangle is 2 metre more than the longer leg. The length of the longer leg is 7 metre more than the length of the shorter leg. Find the number of metre in length of each side of the right triangle. Answered by Stephen La Rocque. 





The base of an isosceles triangle 
20080224 

From tahrima: find the base of an isosceles triangle whose area is 12sq.cm and the length of 1 of the equal sides is 5 cm. Answered by Stephen La Rocque. 





The diagonal of a rectangle 
20080221 

From tim: is there a formula for finding the diagonal of a rectangle? Answered by Penny Nom. 





Two right triangles 
20080218 

From Amy: Hi, I have a problem that has me stumped.
There are two right triangles that share the same adjacent side (AB) which
is 240'. The right angles of each triangle are at the opposite ends of the
shared side.
The Opposite side (AC) of Triangle ABC is 180'
and the Hypotenuse (CB) is 300'.
The Opposite side (BD) of Triangle ABD is 100'
and the Hypotenuse (AD) is 260'.
How do I figure out where the hypotenuses intersect? Answered by Stephen La Rocque and Harley Weston. 





The area of a right triangle 
20080218 

From ASHLEY: WHAT IS THE AREA OF A RIGHT TRIANGLE? WITH THE SHORT SIDE
BEING 16 AND THE HYPOTENUSE 20? Answered by Penny Nom. 





The length of the third side of a triangle 
20080216 

From mary: I have an angle of 72 degrees and each of the sides are 5' long. What is the distance from each of the ends of the 5 feet to form a triangle. Answered by Stephen La Rocque. 





The area of a rectangle 
20080212 

From mark: The diagonal of a rectangle is 15cm, and the perimeter is 38cm. What is the area? It is possible to find the answer without finding the dimensions of the rectangle. Please help me and show as much of the problem as possible. Thank You Answered by Penny Nom. 





A triangle and its incenter 
20080211 

From Elle: In the figure, P is the incenter of triangle ABC, the radius of the inscribed circle is 6cm, and the perimeter of triange ABC is 38cm. What is the area of triangle ABC? Answered by Penny Nom. 





A flagpole and a statue 
20080209 

From Krista: A flagpole casts a ten meter (m) shadow at the same time as a six metre (m) statute beside it casts a two metre shadow. What is the height of the flagpole?? Answered by Steve La Rocque and Penny Nom. 





The width of a rectangle is 4 less than twice its length. 
20080209 

From Shawn: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 72 cm,
what is the length of the diagonal Answered by Stephen La Rocque. 





A three sided shape 
20080209 

From Tim: Question from Tim:
How would I calculate the area in square feet of a "triangle" with sides:
Base is 36 feet; height is 70 feet; and the thirs side is an arch (curve) of 77 feet. Answered by Harley Weston. 





Classifying a triangle 
20080207 

From kevin: scalene triangle 8 ft base right side 9.5 left side 12 ft what is the angles Answered by Penny Nom. 





The radius of a circular arc 
20080204 

From Bill: Hi,the Central Angle of a sector of a circle is 40 degrees. The circular arc of the curve has a chord length of 3000 ft. Find the radius(r) of the circular arc. Answered by Penny Nom. 





The dimensions of a rectangle 
20080201 

From Evan: you are given that the area of a rectangle is 21.6in sq. find the base and the height of the rectangle. Answered by Penny Nom. 





The interior angles of a parallelogram 
20080129 

From amber: the measure of one interior angle of a parallelogram is 42 degrees more than twice the measure of another angle. Find the measure of each angle. Answered by Penny Nom. 





The interior angles of a parallelogram 
20080128 

From steffie: How do you calculate the interior angle sof a parallelogram? Answered by Penny Nom. 





Inscribed square in a triangle 
20080127 

From Adrian: Consider a rightangled triangle PQR, where QR is the base and PQ is the height.
QR=4cm and PQ=3cm. A square is inscribed in this triangle.Determine the length
of one side of the square. Answered by Stephen La Rocque. 





Finding the area of an isosceles triangle given one angle and the inradius 
20080124 

From Saurabh: Given an isosceles Triangle, whose one angle is 120 and inradius is √3. So area of triangle is? Answered by Stephen La Rocque. 





The smallest possible perimeter 
20080123 

From RS: If two points of a triangle are fixed, then how can the third point be
placed in order to get the smallest possible perimeter of the triangle. Answered by Chris Fisher and Penny Nom. 





Number of points with integer coordinates which lie inside the triangle 
20080122 

From Saurabh: Number of points with integer coordinates which lie inside the triange whose verticies are (0,0) , (0,21) and (21,0) ??? Answered by Stephen La Rocque. 





The three angles of a triangle 
20080121 

From val: two angle in a triangle equal 120 degree. what is the measure of the third angle? Answered by Penny Nom. 





Two circles in a rectangle 
20080118 

From Alex: One side of a rectangle is 10 and the other is x.
Two circles with equal radii are inscribed in the rectangle and like a Venn Diagram, the circles overlap.
Each circle touches the top and bottom of the rectangle and the left circle touches the left side of the rectangle and the right circle touches the right side of the triangle.
The distance between the centre of each circle is 2x/3.
Find x Answered by Penny Nom. 





The angles of a triangle given the three sides 
20080117 

From Lucy: Is there a way to find the angles of a triangle just by knowing the lengths of it's sides?
It seems like the would be a relationship between the two, but I'm not sure. Answered by Stephen La Rocque and Harley Weston. 





How tall is the pole? 
20080113 

From Michael: If a 25 foot cable is attached to the top of a pole, and that cable
attaches to the ground ten feet away from that pole, how tall is the pole?
The 25 foot cable is the hypotenuse of a right triangle with a base of
ten feet. Answered by Leeanne Boehm and Penny Nom. 





Forces on an inclined plane 
20080110 

From Ron: A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body? Answered by Stephen La Rocque. 





The height of a triangle 
20080104 

From Dara: The area of a triangle is 54m2. If its base is 5m, find its height. Answered by Penny Nom. 





Lining up coins visually using geometry and trigonometry 
20071231 

From Jessica: a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a halfdollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; halfdollar, 1205.
b) How should the coins be placed, if the distance between the dime and the halfdollar is 100 units?
How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size? Answered by Stephen La Rocque. 





A rectangle is three times as long as it is wide. 
20071231 

From Robert: A rectangle is three times as long as it is wide. If the length is decreased by 2 cm and the width is increased by 3 cm, the new rectangle has an area of 42 cm. What are the dimensions of the original rectangle? Answered by Penny Nom. 





Calculate the two possible lengths of the third side. 
20071228 

From Lisa: An isosceles triangle has an area of 25.6 sq cm.
The two equal sides are 8.4 cm long.
Calculate the two possible lengths of the third side. Answered by Penny Nom. 





The dimensions of a rectangle 
20071222 

From Justin: I'm trying to find the width of a rectangle. I have its area and its height. The area is 32 inches square and the width is 4 feet (48 inches). Can someone help explain this to me? Answered by Penny Nom. 





How many triangles can be formed? 
20071221 

From pankaj: Q.There is 2 lines parallel to each other. If 1st has 5 points in it and 2nd 3 points in it,how many triangles can be formed? Answered by Penny Nom. 





Find the lengths, and explain in a 'let statement' 
20071220 

From Cordilla: the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a' let statement'. Answered by Stephen La Rocque and Harley Weston. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





A triangle and a rectangle 
20071214 

From Someone: A certain triangle has sides that are, respectively, 6inches,
8inches, and 10 inches. A rectangle with a n area equal to that of the triangle
has a width of 3 inches. What is the perimeter of the rectangle, in inches. Answered by Penny Nom. 





Finding all the angles 
20071213 

From Rajesh: An eqilateral triangle is drawn in a square with one of the side as its base and draw the lines from the other angular sides such that there are four triangles
formed inside the square which includes the equilateral triangle.I want to know all the angles of all the triangles formed inside the square. Answered by Stephen La Rocque and Penny Nom. 





A 454590 triangle 
20071213 

From Aaditya: explain to me please how to do the 454590 theorem when one of the legs(not the
hypotenuse) is 3. How do you find the remaining two sides? please help me out. Answered by Leeanne Boehm. 





The dimensions of a rectangle 
20071212 

From tara: The length if a rectangle is 5 feet less than twice its width. The perimeter of the rectangle is 38 feet. let w represent the width. write an equation for the perimeter of the rectangle in terms of w. Then solve the equation to find the length and width o the rectangle. Answered by Penny Nom. 





A right triangle 
20071206 

From Shubhomoy: The coordinates of a hypotenuse are (1,3) and (4,1). Find the equations of the perpendicular sides. Answered by Harley Weston. 





A circle inscribed in a triangle 
20071206 

From Linnea: I have a tringle with a circle inscribed in it. My teacher wants me to find the radius of the circle. This is what she gave me to work with. The triangle is ABC, AB = AC = 6, and BC = 4. She also told us to use A(squared) + B(squared) = C(squared). and that there are altitudes and and incenter. I have no idea how to do this. Answered by Harley Weston. 





Third side of a triangle 
20071205 

From Sudhir: How can we find the all positive integral values for the third side of a triangle, whose other two sides measure 15 and 20 respectively. (No other information viz. the type of triangle, area, perimeter or angles etc. is given.) Answered by Stephen La Rocque. 





Area = 1/2 ab SinC 
20071203 

From Eileen: Given: Acute triangle ABC, with a, b, c, being the respective opposite sides to angle A, angle B, angle C, and altitude, h, drawn from angle B to b.
Prove: The area of trianlge ABC=1/2abSin C Answered by Stephen La Rocque. 





What angle should he turn? 
20071201 

From Jasmine: Bob is traveling due north he then turns left 45 degrees followed by four 20 degree turns to the right
What is his new heading if he needed to turn so his heading was SSW what direction and what angle should he turn? Answered by Walter Whiteley. 





The area of a triangle 
20071130 

From Kevin: if the base of the triangle is 13ft and the altitude is 6ft then what is the area, and how do we calculate this? Answered by Penny Nom. 





Find the centroid 
20071126 

From josh: vertices X(2,6) Y(4,10) Z(14,6) find the coordinates of the centroid Answered by Stephen La Rocque. 





An isosceles triangle 
20071126 

From Nancy: I needed to help my 9th grade daughter regarding a geometry problem. After a while I realized I am not getting anywhere. I saw that in 2005 someone asked the same question and you gave them a hint. Unfortunately it still did not help. Because I had figured that much!Can you kindly help me proof this problem?
PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles?
I am sure it is something simple I am missing, but I just can not seem to be able to see it. Thank you much. Answered by Harley Weston. 





The maximum area of a rectangle 
20071123 

From Christy: Question from Christy, a student:
Show that among all rectangles with an 8m perimeter, the one with the largest area is a square.
I know this is simple but I'm not sure if I'm doing it correctly. Here is what I did.
1. A = xy
2. 8 = 2x+2y
3. y = 4x
4. A = x(4x) = 4xx^2
Not sure what to do from this point because I don't know if its right. Answered by Harley Weston. 





The areas of a rectangle and a triangle 
20071113 

From karen: hoe to calculate the shaded area of a triangle in a rectangle Answered by Penny Nom. 





The third side of a triange 
20071112 

From Christine: I need the inequality to describe the third side of a triange if two sides are known. First side is 23 and second side is 15. What is the third side? Answered by Stephen La Rocque and Victoria West. 





Related Rates (streetlamp and shadow) 
20071109 

From Casey: A street light is mounted at the top of a 15ft pole. A man 6ft tall walks away from the pole at a rate of 5ft per second. How fast is the tip of his shadow moving when he is 40ft from the pole? Answered by Stephen La Rocque and Penny Nom. 





Two triangles 
20071108 

From Barbara: If the base of a larger triangle is 34 inches long, what is the length of side A of the smaller triangle?
(the small triangle has on top the letter a on the right side of the triangle it has the letter b, and at the bottom of the small triangle it has the number 17) Answered by Penny Nom. 





The width of a rectangle 
20071107 

From BJ: The perimeter of a rectangular field is yards. If the length of the field is yards, what is its width? Answered by Penny Nom. 





The height and area of a triangle 
20071105 

From Daniella: I need the exact formulas to find the height, the area,the lenght of triangles... Answered by Penny Nom. 





The height of a triangle 
20071103 

From William: I need to find the height of a triangle if the base is 15, one side is 14 and the other side is 13. Answered by Stephen La Rocque and Penny Nom. 





A right angle triangle 
20071102 

From PRAIMNAUTH: In a right angle triangle , knowing one angle (90 degree ) and the length of the base, how can you calculate the hight and the hypotenuse ? Answered by Penny Nom. 





The base and height of a triangle triangle 
20071031 

From mike: How do you find the length of the base or the height of a triangle if the area is 30 square feet? Answered by Penny Nom. 





The height of an isoceles triangle 
20071029 

From Maura: I am trying to calculate the height of an isoceles triangle but in this case AB is not equal to AC.
How do I calculate this?
Thank you,
Maura age 13 Answered by Stephen La Rocque. 





The length of the side of a triangle 
20071028 

From devon: hay ok i have the height of a triangle but how do i find the length od the side if all of the sides are the same length Answered by Penny Nom. 





An equalateral triangle is 30 acres 
20071028 

From mike: If the area of an equilateral triangle is 30 acres, what is the length of each side in feet or miles? Answered by Penny Nom and Victoria West. 





Area of a triangle formed by three points on a graph 
20071026 

From Betty: My question is 'find the are of a triangle whose vertices have
coordinates (3,5),(6,5), and (4,10) Answered by Stephen La Rocque. 





The length of a rectangle is twice the width 
20071026 

From Tami: The length of a rectangle is twice the width. The number of square units in it's arear is four times the number of units in it's perimeter. What are the dimensions of the rectangle? Answered by Penny Nom. 





Magic triangles 
20071025 

From joshine: i confuse about a magic triangle.but my teacher ask me to make
examples of it in 4 different magic triangle and also different pattern
can you help me about it? Answered by Penny Nom. 





Two mirrors 
20071024 

From Peter: The reflecting surfaces of two intersecting flat mirrors are at an angle θ (0° < θ < 90°). For a light ray that strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle β = 180° – 2θ. Answered by Stephen La Rocque. 





Given a six by six square, how rectangles are there in the square? 
20071024 

From Maria: Given a six by six square, how rectangles are there in the square? Answered by Stephen La Rocque. 





The length of a rectangle 
20071024 

From Kharez: What is the length of a rectangle with an area of 24 square feet and a width of 4 feet? Answered by Penny Nom. 





An equilateral triangle with height 2 inches 
20071023 

From Christine: I'm doing an project in school about tessellations.
But first, I have to construct an equilateral triangle with an altitude of exactly 2 inches.
I know how to draw an equilateral triangle...but I don't know what I have to do in order for the triangle to have an altitude of 2 inches. Answered by Penny Nom. 





Calculate the dimensions of the rectangle 
20071016 

From Sara: The perimeter of a rectangle is 62cm. The length of the diagonal is 25 cm. Calculate the dimensions of the rectangle. Answered by Stephen La Rocque. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





The dimensions of a rectangle 
20071014 

From Elizabeth: The perimeter of a rectangle is 20m. The area is 20sqm. Calculate the dimensions of the rectangle. Give your answers correct to two decimal places. Answered by Penny Nom. 





The angles in a polygon 
20071011 

From Farzan: Prove with induction that in a polygon( that may not be convex )
with n sides, the sum of the amounts of the angles become 180(n2).
If there is any easier methods to prove the problem, please write as well. Answered by Stephen La Rocque. 





Triangle perimeter and area 
20071005 

From divakar: The sides of the triangle are integers. The perimeter is 8. What is the area? Answered by Stephen La Rocque. 





Arc lengths, central angles and radii 
20071004 

From Ashutosh: Jose can remember that the length of an arc is 440cm, but he cannot remember the radius of the arc or the angle at the center. He does know that the angle was a whole number of degrees and the radius was less than 100cm. Find three possible angles and write down the size of each of the possible radii. Answered by Stephen La Rocque. 





Find the area of the traingle 
20071002 

From Indrajit: The perimeter of a triangle is equal to the perimeter of a semicircle of
radius 35 cm.The ratio of the triangles is 5:6:7.
Find the area of the triangle?
[pie = 22/7] Answered by Stephen La Rocque. 





Equation of a circle circumscribing a triangle with given vertices 
20071001 

From Randy: How do I determine the equation of a circle when it is circumscribed by a
triangle whose vertices are (1, 6), (3, 2), and (2, 5)? Answered by Stephen La Rocque. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





An equilateral triangle 
20070913 

From Bibi: An equilateral triangle has a point P inside it. PA, PB, PC are the perpendiculars from point P to the three sides of the triangle. Help me show that PA+PB+PC is the same no matter where the point P is..? Answered by Harley Weston. 





Composite angles 
20070913 

From Gilbert: what is a composite angle? please help Answered by Stephen La Rocque. 





Find the area between (4,0) (2,0) (2,6) 
20070911 

From sabrina: Find the area between (4,0) (2,0) (2,6) Answered by Penny Nom. 





A rectangle inscribed in a circle 
20070911 

From Sobeida: A rectangle that is x feet wide is inscribed in a circle of radius 8 feet. What is the area of the rectangle as a function of x.
Thanks! Answered by Stephen la Rocque. 





A right angles triangle 
20070905 

From Daryl: I have a rightangled triangle. two of its sides are 12.6cm. The third/last line is missing. How can I find the length of the last line? Answered by Stephen La Rocque and Penny Nom. 





Similar triangles 
20070829 

From James: Question: In the triangle ABC, X is a point on AC. AX = 15 m and XC = 5 m. The angle AXB is 60 degrees and the angle ABC is 120 degrees. Find the length of BC.
I am sure to an extent that this has to do with similar triangles, but I am not certain. Answered by Harley Weston. 





Reference angles 
20070825 

From Jenny: find the reference angles for the angles given below, find the quadrants in which the angles lie
1. 0=6n/7
2. 0=3.3 Answered by Stephen La Rocque. 





A geometry problem 
20070820 

From samhita: ABC is a triangle. Let D be a point on side BC produced beyond B such that BD=BA. Let M be the midpoint of AC. The bisector of angle ABC meets DM at P. Prove that angle BAP=angle ACB. Answered by Chris Fisher. 





Area and perimeter 
20070816 

From sheryl: a 50*70 horse pen is 240 feet and 3500 square feet
a 60*60 horse pen is 240 feet and 3600 square feet
why is there a 100 square feet difference? Answered by Penny Nom. 





The area and perimeter of a rectangle 
20070815 

From Brooklyn: Is there a way to find the perimeter of a rectangle if you have the area, or vice versa? If so, what is the equation? Answered by Leeanne Boehm and Penny Nom. 





The length of the third side of a triangle 
20070815 

From Brooklyn: What is the equation to find the length of the third side of a triangle if you have the length of A, B, and the angles(s)? Answered by Stephen La Rocque. 





A right triangle 
20070811 

From Peter: Ok, is it possible to find the height and base of a right triangle when all the information you are given is the length of the hypotenuse?
I also know that the angle between side b and the hypotenuse is 45 degrees. please help. Answered by Walter Whiteley. 





Find the dimensions of the rectangle that will contain the greatest area 
20070806 

From Julirose: The perimeter of a rectangle is 38 meters. Find the dimensions of the rectangle that will contain the greatest area. Answered by Penny Nom. 





The height of a pole 
20070802 

From lalaine: Hi, this is my problem..
From a point 50.2 m to the pole, a student measured the angle of elevation to the top of the pole to be 32°. Find the height of the pole if the student's height from his feet to his eyes is about 4 ft. Answered by Penny Nom. 





Three points on the circumference of a circle 
20070730 

From Bharathi: given a circle with radius r and a point x,y on its circumference,output two other
points x1,y1 and x2,y2 on the circle so thar all 3 points form a equilateral triangle. Answered by Stephen La Rocque. 





Area of a star in a regular pentagon with side length 10cm 
20070724 

From Chetna: A regular pentagon with side 10 cm has a star drawn within (the vertices match).
What is the area of the star? Answered by Stephen La Rocque. 





Angle of depression 
20070723 

From joyce: hello,
here is my problem......
As you stand on a bridge w/c is 100 ft. above the water
you are looking @ an approaching barge.
If the A of top of the front of the bridge is 29.04 degrees
and the angle of depression of the rear is 17.36 degrees .
Find the length of the barge? Answered by Harley Weston. 





An oblique triangle 
20070719 

From fhay: In an oblique triangle, If side a=95, side b=102 and side c = 150 find the missing angles solved by right angles...Thank's a lot...... Answered by Penny Nom. 





Angle of depression (declination) between sailboat observations 
20070718 

From Joyce: From a cliff 150 ft above a lake, we see a boat sailing directly towards us.
The angle of depression of the boat is seen to be 5 degrees and 7 inches and
11 degrees and 18 inches. Find the distance sailed between observations. Answered by Stephen La Rocque. 





Angle of inclination from the horizontal 
20070718 

From Joyce: In flying upward for 1260 yards along a straight inclined path airplane rises
156 yards. Find the climbing angle
( the angle of inclination from the horizontal)
Thank you in advance Answered by Stephen La Rocque. 





The isosceles triangle of largest area with perimeter 12cm 
20070716 

From sharul: find the dimension of isosceles triangle of largest area with perimeter 12cm Answered by Harley Weston. 





Height of a tower from two observations 
20070716 

From joyce: An observer wishes to determine the height of a tower. He takes sight @
the top of the tower from A & B w/c are 5oft. apart @
the elevation on a direct line w/ the tower.
The vertical angle @ point A is 30 degrees & the point B is 40 degrees.
What is the height of the tower?
Find the value of x in angle tangent 40 degrees and 30 degrees?
Show the solution of the value of x? Answered by Stephen La Rocque. 





Height of an antenna (angle of elevation) 
20070716 

From Fhay: An antenna stands on the edge of the top of a 52 story building from a point 320 ft. from the base of the building, the angle of elevation to the top of the antenna is 64 degrees in each story is 12 ft. high. Find the height of the antenna Answered by Stephen La Rocque. 





The two towers (angles of elevation trigonometry) 
20070714 

From joyce: The angle of elevation of tower B from the top of tower A is 28 degrees
and the angle of elevation of the top of tower A from the base is 46 degrees
Find the height of tower A if tower B is 120 m high? Answered by Stephen La Rocque. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Proof that any side of a triangle is less than half the perimeter. 
20070707 

From Omkar: Any side of a triangle is smaller than half of its perimeter, prove this in short ? Answered by Stephen La Rocque. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





Using calculus to prove the formula for the area of a triangle 
20070704 

From Apratim: Using calculus how can one show that the area of any triangle is 1/2 times its base times its height? Answered by Stephen La Rocque. 





A square and an equilateral triangle have the same perimeter. 
20070702 

From eve: I am trying to help my daughter with the following problem: A square and an equilateral triangle have the same perimeter. The sum of one side of the square and one side of the triangle equals 28 cm.
Find the sides of the figures. Answered by Penny Nom. 





Using Heron's Formula to help maximize the area of a triangle 
20070627 

From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston. 





Volume in a triangular water trough 
20070624 

From David: A water trough has sloping sides of length 500mm making it triangular in cross section, with vertical ends. The width at the top is 600mm and the length is 2.0 metres.
(i) Calculate the capacity of the trough, giving your answer accurate to the nearest litre.
(ii) Find out the depth of the water when the trough is half full. Answered by Stephen La Rocque. 





The sum of angles in a square is three hundred and sixty degrees 
20070621 

From victor: can you please send to me a formalize proof for the assertion that, the sum of angles in a square is three hundred and sixty degrees. i will be grateful to hear from you Answered by Stephen La Rocque. 





The perimeter of a triangle 
20070620 

From chelsie: how do i find the perimeter of a triangle given the area, base, and height? Answered by Penny Nom and Walter Whiteley. 





A square and a rectangle 
20070619 

From Clarence: What is the difference between rectangle and a square Answered by Penny Nom. 





Using the Pythagorean Theorem 
20070618 

From cynthia: Hi,
If I have a question with a right triangle and it asks....
If ABC is say 400 miles. How much shorter will the miles be if I travel
from BC?
I don't exactly remember the question but, I would I solve a problem
similiar to this one? Answered by Stephen La Rocque. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque. 





The area of equilateral triangle 
20070605 

From solomon: describe the area of equilateral triangle in terms of its side? solve in two ways. Answered by Stephen La Rocque. 





A regular octagon is made up of 8 identical isosceles triangles 
20070604 

From Alex: A regular octagon is made up of 8 identical isosceles triangles. If the perimeterof each isosceles triangle and the hexagon are 58 cm and 168 com respectively, find the length of the identical sides of the triangle. Answered by Stephen La Rocque. 





How many faces does a triangle have? 
20070604 

From Daniela: how many faces does a triangle have? Answered by Stephen La Rocque. 





Area of an isosceles triangle 
20070601 

From Josh: In a previous question answered by Sue regarding the area of a regular polygon you gave a formula for the area of an isosceles. My question is how did you get this formula? Can you please explain to mean the process that you used to get that formula?
Thanks Answered by Stephen La Rocque. 





Altitudes of scalene triangles 
20070517 

From Chris: Two of the altitudes of a scalene triangle ABC have length 4 and 12.
If the length of the third altitude is also an integer, what is the biggest
that it can be? Answered by J. Chris Fisher. 





Angle of Elevation 
20070510 

From Micky: Two Buildings are on opposite sides of a street 40 feet wide.
The taller of the two buildings is 580 feet tall. The angle of depression
from the top of the tallest building to the shorter building across the
street is 57 degrees. Find the height of the shorter building. Answered by Stephen La Rocque. 





Area of an equilateral triangle 
20070509 

From Diana: how do i find the area of an equilateral triangle when they give us the base? Answered by Penny Nom. 





The dimensions of a rectangle 
20070507 

From Stephanie: The perimeter of a rectangle is 54yds , and the area of the rectangle is 180yds^2 . Find the dimensions of the rectangle. Answered by Penny Nom. 





The vertices of a triangle 
20070502 

From natakie: Find the coordinate of the vertices of a triangle whose sides lie on the following three lines.
2x+5y16=0, 4x3y6=0 and 3x+y+2=0 Answered by Penny Nom. 





The height of a triangle 
20070502 

From Cassie: If you have a scalene triangle with sides measuring 8 units, 6 units, and
10 units (and 10 is the base) how do i find the height perpendicular to the
base of 10? Answered by Penny Nom. 





A triangle problem 
20070423 

From Dimitri: In the triangle ABC, M is the midpoint of AB and N is the midpoint of AC. Prove that CM and BN cannot bisect.
(I can prove it by contradiction if it is a scalene triangle, but i cant seem to prove it for isosceles) Answered by Chris Fisher. 





How can I find out how many sides there are? 
20070423 

From gn: I know the angle measurements of a convex polygon. They are congruent angles. How can I find out how many sides there are? Answered by Steve La Rocque, Penny Nom and Walter Whiteley. 





I am looking for a triangle joke 
20070418 

From deborah: Hi there,
I just found your website. Wow!
I am presenting a triangle presentation on Friday at school and I am looking for a triangle joke to open up the presentation.
Do you have one to share with me? I'm discussing types of triangles if that helps. Answered by Stephen La Rocque. 





A gardener has 140 ft of fencing to fence 
20070416 

From Johann: A gardener has 140 ft of fencing to fence in a rectangular shaped vegetable garden. To plant all his vegetables, the gardener needs more than 825 sq ft of space. What are the possibles values for the length of the rectangle that would meet the space requirements? You may assume that the variable x represents the length of the rectangle. Answered by Stephen La Rocque. 





The angle of depression 
20070414 

From MaryBeth: Two towers are 30 m apart. From the 15th floor, 40 m up, find the angle of depression to the base of the taller tower? I think the answer is 53, but the answer book says 37. Answered by Penny Nom. 





Determine the probability that the triangle is acute. 
20070410 

From Greg: Points A1, A2, . . ., AN are equally spaced around the circumference of a
circle and N >=3. Three of these points are selected at random and a triangle
is formed using these points as its vertices. If N = 2k for some positive integer
k >= 2, determine the probability that the triangle is acute. Answered by Penny Nom. 





I have an isosceles triangle. 
20070410 

From Stephanie: I have an isosceles triangle. The two equal sides are given to me, but not the
base. The equal sides are 12. I have to find the base of the triangle. Help!! Answered by Stephen La Rocque. 





A right triangle 
20070405 

From Lee: What would be the length of the long side of a right angle triangle if one side was 47cm and the other was 56cm.
Many Thanks Answered by Steve La Rocque and Jaymi Peterson. 





What is the hypotenuse of a right traingle 
20070404 

From debbie: what is the hypotenuse of a right triangle with sides of 38 meters and 24.2 meters. Answered by Stephen La Rocque. 





Interior and exterior angles 
20070402 

From Anuj: If in a regular polygon, each exterior angle is twice the interior angle,find the number of sides? Answered by Leeanne Boehm. 





Find the measure of all 3 angles. 
20070328 

From Brittney: The smallest angle in a triangle is onethird of the largest angle. The third angle is 10 more than the smallest one. Find the measure of all 3 angles. Answered by Stephen La Rocque. 





The angles in a right triangle 
20070328 

From Golaan: I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length.
I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters.
I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?
The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Answered by Penny Nom. 





The height of a pole 
20070322 

From clyde: I am trying to determine the height of a pole by using 3 angles top 30.8 deg, center 17.3 deg, and bottom 5.8 deg. Can you point me in the right direction ? Answered by Stephen La Rocque. 





The Reuleaux Triangle 
20070322 

From Dani: Hi!
My question is:
Determine how the area of the Reuleaux Triangle of width h compares to the area of a circle of width h?
Thanks!
Dani Answered by Penny Nom. 





Angles of depression 
20070321 

From romaine: a woman of height 1.4m standing on top of a building of height 34.6m veiws a tree some distance away.
she observes that the angle of depression of the bottom of the tree is 35 degrees, and the angle of depression of the top
of the tree is 29 degrees. assume that the building and the tree is on level ground.
(a) calculate the distance of the woman from the top of the tree measured along her line of sight.
(b) determine the height of the tree. Answered by Stephen La Rocque. 





A triangle 
20070318 

From Farzana: pointsA(1,0),B(8,0),C(3,4) are the vertices of a triangle.What is the of this triangle? Answered by Stephen La Rocque. 





A river crossing 
20070316 

From tara: A river has a constant current of 4 kilometers per hour. At what angle
to a boat dock should a motorboat, capable of maintaining a constant
speed of 20 kilometers per hour, be headed on order to reach a point
directly opposite the dock? If the river is 1/2 kilometer wide, how long
with it take to cross? Answered by Stephen La Rocque. 





An isosceles Triangle 
20070315 

From Devon: The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs. Answered by Stephen La Rocque. 





Triple angle tangent formula 
20070315 

From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom. 





The dimensions of a rectangle with least perimeter for given area 
20070314 

From Karlianna: find dimensions of a rectangle with least perimeter for given area
A) 30cm2
b) 50cm2 Answered by Penny Nom. 





Angle of elevation 
20070313 

From Joslyn: A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level.
If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore. Answered by Haley Ess. 





Can the triangle be called both an acute triangle and an equilateral triangle? 
20070310 

From Jane: If all sides of a triangle are the same length and all angles are 60 degrees, can the triangle be called both an acute triangle and an equilateral triangle? Answered by Walter Whiteley. 





Finding the vertical height of a roof 
20070305 

From Zainab: The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o Answered by Stephen La Rocque. 





The area of an inscribed triangle 
20070302 

From Caitlin: What is the area of an equalateral triangle inscribed in a circle whose circumference is 6 pie?? PLEASE HELP Answered by Penny Nom. 





sin(3a), cos(3a) and tan(3a) 
20070228 

From mailene: hi, i...indeed,to..need..your..help how..cn..i..prove..this,formula??? sin3a=3sina4sin^3a cos3a=4cos^33cosa tan3a=3tantan^3a /13tan^2a the..symbol...^is..the..expOnent Answered by Haley Ess and Penny Nom. 





The three sides of a right triangle 
20070223 

From Sharon: I know the hypotenuse of a right triangle is a^2 + b^2 = c^2 but when I replace this with the numbers given, I can't solve it.
Here is my question: The hypotenuse of a right triangle is 2.8 units long. The longer leg is 1.9 units longer than the shorter leg. Find the lengths of the sides of the triangle. Answered by Pam Fowler and Penny Nom. 





The three sides of a triangle 
20070223 

From Christopher: If two sides of a triangel have lengths 4 and 9, then the length of the third side may be any number: a) Less than 13 b) Greater than 5 but less than 13 c) Greatehr than 4 but less than 9 d) Greater than 5 Answered by Haley Ess. 





Similar triangles 
20070221 

From Vivienne: The lengths of the sides of a triangle are 8, 15, & 17. If the longest side of a simlar triangle is 51, what is the length of the shortest side? Answered by Stephen La Rocque and Penny Nom. 





Find the area of the triangle 
20070220 

From Christina: Graph the function f(X)= x+1/x1 and graph the tangent line to the function at the points A:(2,3) and B:(1,0). The point of intersection of the two tangent lines is C. Find the area of the triangle ABC. Answered by Stephen La Rocque. 





Square centimeters 
20070212 

From Ivan: how many square centimeters are in a rectangle that is 210 centimeters long by 39 centimeters wide.? thank you Answered by Karen McIver and Melanie Tyrer. 





Area of a rectangle 
20070207 

From kyle: paul has enough material to make a fence 22 feet long. he will use this material to fence of a rectangular section of his yard. the rectangles sides must all be whole numbers. i am having a hard time finding the greatest and the least area that he can enclose his fece Answered by Haley Ess. 





The interior angles of a parallelogram 
20070207 

From jenniffeir: Can a parallelogram have two 45 degree angles and two 75 degree angles? Answered by Haley Ess. 





A triangle inscribed in a semicircle 
20070206 

From Benneth: Consider a triangle inscribed in a semicircle with a radius of R. What are th possible perimeters for the triagle? And the areas? Answered by Penny Nom. 





Angle of elevation 
20070205 

From Zee: A 55 ft. flagpole casts a 25 ft. shadow. Calculate the angle of elevation to the sun to the nearest degree. Answered by Stephen La Rocque. 





A rectangle inscribed in a circle 
20070204 

From Benneth: Consider a rectangle with radius R inscribed in a circle. What are the possible areas of the rectangle? Answered by Steve La Rocque and Walter Whiteley. 





Rectangles and squares 
20070131 

From Shelby: I am doing homework and I need to know why squares are rectangles but not all rectangles are squares? Answered by Penny Nom. 





Angle of clock hands 
20070131 

From Sophia: How many degrees are in the aute angle formed by the hands of a clock at 2:20 p.m.? Answered by Stephen La Rocque. 





The perimeter and area of a right angled triangle 
20070131 

From Naveen: I need to calculate the area of a right angled triangle. However the measurements of the 3 sides is missing. All we are told is that the perimeter of the triangle is 1000cm. Answered by Penny Nom. 





A thin wire 20 centimeters long is formed into a rectangle 
20070129 

From Trisha: a thin wire 20 centimeters long is formed into a rectangle. if the width of this rectangle is 4 centimeters, what is the length? Answered by Penny Nom. 





Height of a right triangle? 
20070129 

From Engelbert: The base of the right triangle is 50 ft. At the angle (on the base of the triangle) across from the right angle is labeled portion (a triangle within a triangle), the base of this little triangle is 10 ft. and the height is 6 ft. What equation can i use to solve this? Answered by Steve La Rocque and Haley Ess. 





A right triangle 
20070129 

From Tayler: One leg of a right triangle is 8 cm. less than the hypotenuse while the other leg is 1 cm. less than the hypotenuse. Find the length of the hypotenuse. Answered by Penny Nom. 





The height of an isosceles triangle 
20070127 

From Brendan: I need to find the height of an isosceles triangle whose angles are 52, 52 and 76 degrees. The base is 100, and the two equal sides are unknown. How would I go about this? Answered by Stephen La Rocque. 





The area of a scalene triangle 
20070120 

From Kalsi: I have a scalene triangle in which i have to find the area. Answered by Penny Nom. 





The height of a triangle 
20070117 

From Sharon: I am needing to determine the height of a triangle with a 50 ft base and one side is 40 ft the other side being 30 ft. Answered by Penny Nom. 





The height of a triangle 
20070114 

From Shanelle: I'm trying to find the height of a triangle but i only know the base and one of the sides as well as the angle between those two sides...but how can i find the height? Answered by Penny Nom. 





In the shadow of a building 
20070111 

From Bill: if a building b feet cast a shadow f feet long, then, at the same time of the day, a tree t feet high will cast a shadow, how many feet long? Answered by Stephen La Rocque. 





One leg of a right triangle 
20070111 

From Eric: I have a right triangle and the only known leg is one leg adjacent to the right angle. The question is how to find either of the other angles? Answered by Penny Nom. 





Find the area of the rectangle 
20070109 

From Mike: The perimeter of a rectangle is 72 in. The base is 3 times the height. find the area of the rectangle? Answered by Penny Nom. 





Are all rectangles trapezoids? 
20070105 

From Sarah: Are all rectangles trapezoids? Answered by Chris Fisher. 





Where do the medians of a triangle meet? 
20070102 

From Brittany: Where do the medians of a triangle meet? 1. Inside the triangle v 2. On the traingle 3. Outside the traingle Answered by Stephen La Rocque. 





How do the perimeters of the two pentagons compare? 
20070102 

From Robert: If the area of one pentagon is eightyone times the area of another pentagon, how do the perimeters of the two pentagons compare? Answered by Penny Nom. 





An octagonal birdhouse 
20061230 

From Verner: I am building a octagon birdhouse,what degree would I cut each side of each piece of wood to assemble the birdhouse? Answered by Penny Nom. 





The area of a triangle 
20061229 

From Paula: The area of a triangle is 24cm². Its height is 2cm more than its base. Determine the base and the height. Answered by Penny Nom. 





An isosceles triangle 
20061229 

From Katrina: Is there any way to calculate the height or the length of the equal sides of an isosceles triangle given only the base length and the angles? Answered by Penny Nom. 





A quuadratic equation 
20061222 

From Harold: L=3w4 A=96Square I used the quadratic equation to solve and my answer is still wrong
I convert the square of 1168 to decimal.
here is where i start (3w4) x w=96
could you give me an example Answered by Stephen La Rocque. 





The sum of the angles in a triangle 
20061212 

From Becky: Why does a triangle always equal 180 degrees? We know that all the angles add up to 180 degrees but cant find a valid reason for it. Answered by Penny Nom. 





The height of a triangle 
20061201 

From Jeni: I need to know how to figure out the height of a triangle when all I know are the sides and base. The sides are 5 and the base is 8 What do I do? Answered by Penny Nom. 





A triangle problem 
20061129 

From Ann: Triangle FUN has A) 72.8 B) 65.2 C) 72.7 D) 65.3 Answered by Chris Fisher. 





Creating a triangle in a circle 
20061128 

From Dirk: My daughter has a school project where she must draw a circle and then draw an equilateral triangle inside the circle. She said you have to identify six points on the circle to correctly draw the triangle. How do you accomplish this? Answered by Penny Nom. 





Dimensions of a rectangle 
20061122 

From Terri: How can you find the dimensions of a rectangle that has a perimeter of 18 feet? Answered by Stephen La Rocque. 





A right angled triangle 
20061122 

From Siddhartha: area of a right angled triangle OAB where OA = 5 and OB = 3 Answered by Penny Nom. 





The height of a building 
20061119 

From Sweetie: I have to figure out the measure of the water towers antenna on my schools campus using up to two items created by me and a manual. I don't know far away we are going to have to be. I need to have a fool proof way to figure out the distance to the tower. I have an idea using trigonometry but its really roughly estimated. Do you have any suggestions? Answered by Stephen La Rocque. 





The name of a shape 
20061111 

From Valentina: I have a shape of 4 sides 3 are the same length (2cm each) and the other smaller (1.5cm) Answered by Chris Fisher. 





The dimensions of a rectangle 
20061102 

From Ben: A rectangle's length is 8 cm. greater than its width. Its perimeter is 128 cm. Find its dimensions. Answered by Penny Nom. 





The height of a triangle as a function 
20061019 

From Ryan: Let 2s denote the length of the side of an equilateral triangle. Express the height of the triangle as a function of s Answered by Penny Nom. 





How do you find the length and width of a rectangle if you know ... 
20061015 

From Anne: How do you find the length and width of a rectangle if you know the perimeter of the rectangle is 48 m and the area is 144 m squared? Answered by Stephen La Rocque and Penny Nom. 





A 5x2 rectangle 
20061003 

From Stanley: Cut a 5x2 rectangle into 4 pieces, and then put them back into as a square. Answered by Claude Tardif and Penny Nom. 





The hypotenuse 
20061002 

From Ashley: How do you find the hypotenuse of a right triangle? I don't understand how to find c. Answered by Stephen La Rocque. 





a _________________ line forms a 90 degree angle with another line 
20060924 

From Lisa: a _________________ line forms a 90 degree angle with another line is this to it
what fills in the blank? first letter is E third letter is R and has 13 letters Answered by Stephen La Rocque. 





An equilateral triangle has been wedged in between two circles. 
20060922 

From Kim:
An equilateral triangle has been wedged in between two circles. How does the diameter of the smaller circle compare to the diameter of the larger circle.
image: circle inside of an equilateral triangle touching all sides of the triangle; both the triangle and the circle inside are placed into a larger circle where the triangle vertices all touch the circle
Answered by Penny Nom. 





The length of the third side of a 45 degree Isosceles triangle 
20060920 

From Rusty: what is the formula to determine the length of the third side of a 45 degree Isosceles triangle? Answered by Penny Nom. 





How large is the property? 
20060920 

From Jahn: a triangular lot has 750 feet on one side of a 90degree angle and 500 feet on the other side of the angle. how large is the property? Answered by Penny Nom. 





A rectangular tank 
20060919 

From Milton: What size rectangular tank will I need to hold 841.5 gallons of water. The water level is 3'0" from the bottom of tank. Answered by Penny Nom. 





The length of 2 sides of a triangle 
20060915 

From Lonnie: I need to know how to figure the length of 2 sides of a triangle, as the following example:
The length of the bottom is 12' and the angles are 45, 45 I need to know how long the other 2 sides must be to get an angle of 90 at the top. Answered by Stephen La Rocque. 





The volume of a triangular box 
20060912 

From Irene: How do I find the volume of a triangular box? Answered by Penny Nom. 





The area of a triangle 
20060901 

From Anthony: I WOULD LIKE TO KNOW THE AREA OF A TRIANGLE THAT IS 42" AT THE BASE WITH EQUAL SIDES OF 29" . Answered by Stephen La Rocque. 





How do i get the height of an isosceles triangle? 
20060829 

From Luis: How do i get the height of an isosceles triangle? Answered by Penny Nom. 





How high (in feet) is the mountain? 
20060829 

From Briana: A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 31 degrees.
How high (in feet) is the mountain? Answered by Stephen La Rocque. 





Mini Golf 
20060817 

From Sarah: I am a sixth grade teacher in Minnesota. I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level. Answered by Stephen La Rocque. 





An angle in a parallelogram 
20060813 

From Sam: Parallelogram ABCD has diagonal AC equal in length to side AB. CD is produced to E so that D is between E and C. If angle BAC =30 degrees find the size of angle ADE. Answered by Stephen La Rocque. 





How fast is the water level rising 
20060812 

From Erin: Water runs into a conical tank at the rate of 9ft^{3}/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r^{2} h). Answered by Penny Nom. 





A triangle problem 
20060806 

From A student: A triangle is such that its medium side is twice as long as its shortest side, and its longest side is three times as long as its shortest side. The perimeter of the triangle is 54 yards. What are the lengths of the three sides? Answered by Penny Nom. 





How do I draw the arc? 
20060722 

From Dani: How do I draw the arc (calculate the included angle) when I know only the arc length? Answered by Stephen La Rocque. 





Mini Golf geometry 
20060718 

From Sarah: I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level.
If you can steer me towards any resources, I'd be most grateful. Answered by Natasha Glydon. 





The dimensions of a rectangle 
20060709 

From Lori: The length of a rectangle is 1 cm more than 3 times its width. If the area of the rectangle is 61 cm2, find the dimensions of the rectangle to the nearest thousandth. Answered by Penny Nom. 





Isoperimetric quotients 
20060707 

From Jessica: How do you work out an algebraic equation for the IQ of an isosceles triangle. Answered by Penny Nom. 





Order of operations 
20060629 

From Jaden:
(1) A triangle has vertices at (3,3) (7,3) and (2,5). What is the area of the triangle?
Is there a way of doing this so that you dont have to graph it? If the x axis is horizontal can i say it is the base and the yaxis is horizontal meaning the height. Would I be able to do this...3 to 7>9 spaces, 3 to 5>7 spaces9(7)63/2=31.5
(2) A cube has a surface area of 54 square centimeters. What is the volume of the cube in cubic centimeters?
Answered by Stephen La Rocque. 





The area of a sector and a triangle 
20060623 

From Howard: I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord. Answered by Stephen La Rocque and Penny Nom. 





Designing a garage 
20060608 

From A builder: I'm currently designing a garage and came upon this interesting math problem. I've tried using various methods to solve it but have so far been unsuccessful. I've included a picture as its far easier to show you my question than explain it verbally. I realize it could be done by trial and error but i'm looking for a real solution. Answered by Stephen La Rocque and Penny Nom. 





The area of a 30, 60 90 triangle 
20060524 

From Willetta: if there is a triangle with a 30, 60, and 90 degree angle and the shortest side is 6cm how do you find the area? Answered by Stephen La Rocque and Penny Nom. 





The area of a triangle 
20060521 

From A student: how do you find the area of a triangle? Answered by Penny Nom. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





A triangle problem 
20060518 

From Jim: Right angle triangle with a hypotenuse of 20 units.
Square inside the triangle with sides of 4 units, the square shares two sides with both legs of the triangle, and the corner touches the hypotenuse limiting the triangles size. Answered by Penny Nom. 





What is the measure of the interior angles of a decagon? 
20060510 

From Malissa: What is the measure of the interior angles of a decagon?
And what is the measure of each interior angle of a regular decagon? Answered by Stephen La Rocque. 





The last slice of pizza 
20060427 

From Lori: I have a pizza. The radius is 10 inches long.The pizza was cut into 16 equal slices. When one slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.
How far up the radius from the center of the circle will I need to cut so we will both have an equal area of pizza? Answered by Stephen La Rocque. 





Ladder and wall 
20060427 

From Lori: A 12foot ladder is leaning across a fence and is touching a higher wall located 3 feet behind the fence. The ladder makes an angle of 60 degrees with the ground. Find the distance from the base of the ladder to the bottom of the fence. Answered by Stephen La Rocque. 





Finding the supplementary angles 
20060422 

From Kendra: Angles ABC and DBA are supplementary. If m Answered by Stephen La Rocque. 





Perimeter of a triangle atop a square 
20060413 

From Mary: There is an (irregular) pentagon that is made up of a square and a triangle. The triangle is directly on top of the square. The triangle is a right triangle. One of the angles is 45 degrees. One of the sides of the triangle is 4. What is the perimeter of the pentagon? Answered by Penny Nom. 





Finding the side of a triangle 
20060406 

From Carole: okays, well, im having difficulty finding the side of a triangle. It is a right triangle and the information given is that the hypotonous is 24 and the angle adjacent to the 90 degree is 32. Im trying to find X, which is placed on the bottom leg of the triangle, and have no idea how to do it. can you explain to me how to get the answer, please? i'd like to know for future reference, please. thank you. Answered by Stephen La Rocque. 





The height of an isosceles triangle 
20060401 

From Chris: how do you work out the height of an isosceles triangle if i know the length of the base but i don't know any angles or the lengths of the sides? Answered by Penny Nom. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





The area of a triangle 
20060326 

From Colby: the length of one side of a triangle is 2cm less than twice the length of the altitude to that side. the area of the triangle is 30 cm squared. find the length of the altitude.
first of all, what is an altitude? and how do i find it? Answered by Penny Nom. 





Solve the equation cos x = sin 20 where x is acute. 
20060326 

From Elle: Solve the equation cos x = sin 20 where x is acute. Answered by Stephen La Rocque. 





Can an equilateral triangle have an obtuse angle? 
20060326 

From Chris: Can an equilateral triangle have an obtuse angle?
I'm thinking not, because all sides must be equal, but
does that also imply that all angles are equal?
Answered by Stephen La Rocque. 





The volume of water in a cone 
20060321 

From Ghulam: A vessel has the shape of an inverted cone.The radius of the top is 8 cm and the height is 20 cm. Water is poured in to a height of x cm.Show that if the volume of the water is V cubic cm,then V=(4/75)pi x3. Answered by Penny Nom. 





Three towns are located at the vertices of an equilateral triangle 
20060320 

From A student: three towns are located at the vertices of an equilateral triangle. The towns are 8, 5, and 3 miles, respectively, from a store. How far apart are the towns? Answered by Chris Fisher. 





Rectangles with the same perimeter 
20060314 

From Kristine: If two rectangles have the same perimeter, will they also have the same area? Why Answered by Penny Nom. 





Heights and shadows 
20060306 

From Debra: A person is 7 ft tall and his shadow is 10 ft tall. using the same info what is the shadow of a person who is 5ft tall
Answered by Stephen La Rocque. 





An equilateral triangle and a regular hexagon 
20060228 

From Trevor: An equilateral triangle and a regular hexagon have equal length perimeters. What is the ratio of their areas? Answered by Penny Nom and Stephen La Rocque. 





Cutting off the top of a triangle 
20060222 

From Ken: I'm a creative type who needs to find how you can determine the horizontal, relative percentages within a triangle. Attached is a pdf showing approximately the
50% line, but I'd like to know how to determine any percentage (horizontally) within a triangle . I know that if I put a horizontal line though the height of the triangle I won't be showing 50% above and 50% below. The bottom part has to be larger (correct me if I'm wrong).
I'm not concerned about height as I am wanting to break down the percentages into 60% at the bottom, 25% in the middle and 15% at the top.
Answered by Penny Nom. 





A triangle of 50p pieces 
20060222 

From Stuart:
Ok, so i am collecting 50p pieces and arranging them on my desk in the shape of a triangle.
eg
50p
50p 50p
50p 50p 50p
50p 50p 50p 50p
I want to work out how much money I'm saving just by knowing how many rows of coins there are. If i can work out how many coins there are just by knowing how many rows I have I can just divide by 2 to find out the amount in dollars.
Answered by Penny Nom. 





Translate and magnify a triangle 
20060219 

From A student: Triangle CAT has vertices located at C(2,5), A(5,1), T(1,1)
Translate triangle CAT 4 units right and magnify the triangle by 3. List the new coordinates and explain the process of computing the new coordinates.
Graph triangle CAT and the new triangle form part A on the same coordinate plane....
Will the area of the new triangle be 3 times as large as the original?? Explain why or why not Answered by Penny Nom. 





The third side of a triangle 
20060209 

From Clayton: How do I find the length of the third side of a triangle if a=30m, b=30m and I need to find c? Answered by Steve La Rocque and Penny Nom. 





How do you find the angles in a triangle? 
20060127 

From Keith: How do you find the angles in a triangle if you know the lengths of the sides? Answered by Chris Fisher and Penny Nom. 





how can i find the height of a triangle if i have the base and the hypotenuse 
20060127 

From Kelsey: how can i find the height of a triangle if i have the base and the hypotenuse Answered by Penny Nom. 





Subdividing a polygon into triangles 
20060126 

From Adam: is there an algorithm to divide a regular polygon into N
equilateral triangles having the same area (no limit on N), or if not, an
algorithm to divide a regular polygon into N triangles having the same shape
and size? Answered by Chris Fisher. 





The third side of a triangle 
20060125 

From Bob: Is there any way to obtain the third side of a triangle when 2 sides are the same length (2.18 inches). I also need to find the angles. Answered by Penny Nom. 





Right angles 
20060125 

From AshLee: I was recently given a challenge in my Algebra class. My teacher wanted to know about a right angle. He said he would give five bonus points to the person that could bring in information. (I know five bonus points may not seem like a lot but in this class, they are.) I looked on this site and I found out why it was called a right triangle, but my teacher want to know where did that theory come from. I was wondering too... not just because of the bonus points. Answered by Penny Nom. 





The three angles in a triangle 
20060123 

From A student: the measure of the 2nd angle in a triangle is 4 more than the measure of the 1st angle. the measure of the 3rd angle is eight more than twice the measure of the 1st angle. find the measure of each angle. Answered by Penny Nom. 





The angles in a hexagon 
20060122 

From Linda: My problem is in relation to wood and making a six sided object from it. On my saw, there is a place to set the angle to which you wish to cut. I cannot for the life of me, figure this out. I am starting with a piece of plywood (1/4" x 6" x 18") and need to know what the angle degree would be to make each of the sides match perfectly to form a hexagon. Trial and error just is not working. Can someone help me? Answered by Penny Nom. 





The centroid of a triangle 
20060118 

From Andrea: I am trying to find the centriod of a triangle. I have been given the three vertices of the triangle: A (25, 20), B (5, 40), and C (15, 30). I believe I calculated the correct midpoints: AB(E) (5, 5), BC(D) (5, 5), and AC(F) (15, 30). When I graphed these points I came up with the solution (5, 10), but I can't seem to write the answer out (equations of the lines, etc) correctly. Any help would be greatly appreciated! Answered by Penny Nom. 





Interior and external angles of a polygon 
20060117 

From Anthony:
In a regular polygon, the ratio of the interior angles to the exterior angles is 3:1.
(a) Find the measure of the interior angle.
(b) How many sides are there
Answered by Penny Nom. 





The height of a triangle from the lengths of the sides 
20060116 

From A student: How do you figure out the height of a triangle when all you have is the length of the sides of the triangle? Answered by Claude Tardif. 





How do I find the area with only one sides measurement? 
20060110 

From Amy: If you have a right triangle with the 90 degree angle located in the bottom left corner and the triangles most sloped line goes from the top left down to the right bottom. And the length of the slope line is 10(radical sign)with the radicand of 2. How do i find the area with only one sides measurement. Answered by Penny Nom. 





The height of a right triangle 
20051221 

From Sanmantha: I am trying to solve for the height of a right triangle. The base is .05 mm, and the apex is 0.5 degrees. I vaguely recall from high school that this should be enough information to solve for height, but I can't remember what equation(s) to use. Answered by Penny Nom. 





A rectangle has a length that is 7cm more than twice the width 
20051221 

From Stephanie: A rectangle has a length that is 7cm more than twice the width. The area of the rectangle is 60cm squared. Find the dimensions of the rectangle. Answered by Penny Nom. 





The sum of the angels in a triangle 
20051125 

From Rachel: how do you prove, without knowing any of the measurements or degrees, that the three angles of a triangle equal 180? what are the steps for proving that? Answered by Penny Nom. 





Find the measure of each angle 
20051125 

From Bev: in triangle abc, angle a is four times as large as angle b, angle c measures 20 degrees less than angle b. find the measure of each angle. Answered by Penny Nom. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





A variable rectangle 
20051108 

From Mussawar: find the lengths of the sides of a variable rectangle having area 36 cm^{2} when its perimeter is minimum i do not want solution of this question. i would like to know what is mean by variable rectangle.and what is difference between rectangle and variable rectangle.also what is mean by when its perimeter is minimum. Answered by Penny Nom. 





The height of a tower 
20051108 

From Vinita: Observers at point A and B, who Stand on level ground on opposite sides of a tower, measure the angle of elevation to the top of the tower to be 33 degrees and 49 degrees respectively. Another point C is 120 m from point B, Triangle ABC =67 degrees and BAC = 31 degrees. Find the height of the tower to the nearest metre. Answered by Penny Nom. 





Triangles with integer sides 
20051104 

From Tammy: I am trying to find another pair of integer sided isosceles triangles, not the same as the ones listed below, with equal areas.
(5,5,8)
(5,5,6) Answered by Chri Fisher. 





What is the angle between 2 noncollinear parallel lines? 
20051017 

From Ben: What is the angle (if any) between 2 noncollinear parallel lines? Answered by Chris Fisher and Walter Whiteley. 





What is the sum of the measures of the angles of a decagon? 
20051015 

From Dianna: What is the sum of the measures of the angles of a decagon? Answered by Penny Nom. 





Constructing figures 
20050920 

From Kim: I would like to know how to draw different shapes:
Regular Octagon with sides of length, 1 unit
Equilateral Triangles, with sides of length 1 unit
Regular Hexagons, with sides of length 1 unit
Isoseles Triangles, with hypotenuse of length 1 unit
Answered by Penny Nom. 





A 306090 triangle 
20050911 

From Gary: I have the length of only 1 side of triangle with angles of 306090 degrees. How can I find the length of the other 2 sides? Answered by Penny Nom. 





The length of a chord 
20050908 

From A student: how do you find the length of a chord given the angle and radius of the circle Answered by Penny Nom. 





The area of a triangle 
20050826 

From Martha: I have a triangle that with a base of 60' and the two sides of 37'. I know the formula for area is A=1/2 (b*h) but how do I find the height??
Answered by Penny Nom. 





Is 360 Really the correct value? 
20050815 

From Jack: Considering the circumference of a "Perfect Circle" with a Diameter of 1 meter would be something like 3.14 meters, why do we use the number 360 to represent the number of degrees within that circumference?
Would it not make more sense to express the degrees in reference to the relationship to the diameter as related to pi?
That is, let's just say our "Perfect Circle" has a circumference of 3.14 meters, therefore, what we now consider as due east would change from 90 Degrees to 78.5 Degrees. Answered by Penny Nom. 





A right triangle 
20050518 

From Bill: If I know the base and the slanted side of a right triangle, how do I figure out the height? Answered by Penny Nom. 





Angle of incline 
20050515 

From Kyle: What is the degree of incline of a 12 foot plank that goes from 10.5 inches on one end to zero inches on the other? Answered by Penny Nom. 





sin x + sin 2x + sin 3x + sin 4x = 0 
20050510 

From Elia: I tried many times, but can't get to solve the following question:
sin x + sin 2x + sin 3x + sin 4x = 0 Answered by Chris Fisher. 





Some triangle problems 
20050506 

From A student: 1.use the
heron's formula to find area of triangle ABC to nerest tenth
A.a=21 b=28 c=11
B.a=23 b=28 c=12
2.Find the nearest tenth the altitude of the longest side if a=3 b=3 c=5
3.the length of each side of a rhombus is 10 cm the length of one diagonal
is 12 cm find the area to the nearest square centermeter Answered by Penny Nom. 





An isosceles triangle...with 
20050423 

From Shannon: If given an isosceles triangle...with
Is there any possible way to do this, without knowing a side, if so, please
explain in detail. Answered by Chris Fisher. 





cos(2x) = sin(3x) 
20050414 

From A student: Show that if x= 18 degrees, then cos2x =sin 3x. HENCE find the exact value of sin 18 degrees, and prove that cos 36  sin 18 =1/2. Answered by Andrei Volodin, Claude Tardif and Penny Nom. 





The centroid of a triangle 
20050407 

From Maria: Q3)find the coordinates of the centroid of triangle ABC
i want your help here to solve the 3rd question i got stuck. Answered by Penny Nom. 





A triangle question 
20050226 

From John: H=10' 7and3/4",angleX=30 degrees solve for the adjacent side Answered by Penny Nom. 





Each interior angle of a particular polygon is an obtuse angle... 
20050222 

From Victoria: Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have? Answered by Walter Whiteley. 





A 6 sided (hexagonal) pyramid 
20050122 

From Steve: im trying to make a 6 sided (hexagon) pyramid, from 6 triangles of 12mm plywood, i know all the angles to cut apart from the one one to join all 6 triangles together. Rough measurements are outer edge (A) of each triangle is 13cm's, length of other 2 sides (B&C) of triangle outside to center is 14cm's with a height of the whole thing together about 6cm's. Answered by Chris Fisher and Harley Weston. 





The area of a triangle 
20050121 

From Amy: In tirangle ABC, AB=6, BC=9, BC is the angle bisector of angle ABC and M is the midpoint of BD. If the area of ABC is 30, what is the area of ABM?
The height comes out greater than the hypotenuse, but the teacher said that there's an answer for it. Can you show me how? Thanks Answered by Chris Fisher. 





Finding the missing side of a triangle 
20050120 

From Jason: I found a geometry problem that reads as follows:In triangle ABC, Answered by Penny Nom. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





A geometry problem 
20050101 

From Alexandra: In triangle ABC, b=40, and angle A= 30 degres. What values of BC will give two solution for angle B? Answered by Penny Nom. 





The area of a triangle 
20041230 

From Perry: What is the area of a triangle with dimensions 3"X5"X7"? Could you provide the formula? Answered by Penny Nom. 





A Reuleaux triangle 
20041222 

From Bob: I am trying to remember the name given to the regular figure constructed from three arcs. The figure is like an equilateral triangle except with arcs for each side. Answered by Chri Fisher. 





A right triangle 
20041124 

From Bruce: In triangle ABC.
Angle ABC is 90 degrees.
Side AB measures 34.
Side BC measures 31.
What does side AC measure? Answered by Penny Nom. 





Is a square a rectangle? 
20041121 

From Carol: I am a teacher. In an FCAT sixth grade review test, there was a question to the students to draw a square and then they referred to it as a rectangle.
What is the definition that makes a rectangle a square that can be taught to the students without confusing them. Answered by Walter Whiteley. 





Interior and exterior angles of a polygon 
20041116 

From Aaron: How do you find the measure of interior and exterior angles of a regular polygon when you are given the number of sides? Answered by Walter Whiteley. 





A 306090 triangle 
20041109 

From Amy: How do you find the length of the hypotenuse of a 306090 triangle when the side opposite the 60 degree angle is 6 inches? Answered by Penny Nom. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom. 





Two gears 
20041014 

From Lindsay: "There are two gears, a small one on the left and a larger one on the right. The gear on the right makes 1 revolution. The gear on the left makes two revolutions. Suppose the gear on the right is turned through an obtuse angle. Will the gear on the left make a full turn?" Answered by Penny Nom. 





The length of a rectangle 
20040926 

From Rebecca: My question is each side of a square S is 18 inches long and the area of S is at least 3 times the area of a rectangle that is 9 inches wide. What is the greatest possible length in inches of the rectangle? Answered by Penny Nom. 





Supplementary angles 
20040923 

From Rosemary: Is the term supplementary angles only applicable to 2 angles (ie. a pair of angles) or can it be used when talking about 3 or more angles that add to make 180 degrees? Answered by Penny Nom. 





The hypotenuse of a right triangle 
20040920 

From Shannon: I am trying to find the hypotenuse of a right triangle with only the length of the opposite side. What is the formula as I don't have the length of the adjacent side? Can I compute it without knowing what the other two angles are? Answered by Penny Nom. 





Fabricating with pipe 
20040919 

From Gil: I need to fabricate a 10 section, 4" pipe circle with an inside diameter of 40". I would like to know what angles would apply and how to find them, Answered by Penny Nom. 





Finding the height of a triangle 
20040914 

From A student: I have to calculate the height of a triangle.
The base is 6 (units)say ab
One of the top sides is 4 (units)say ca
The other side is 2 (units) say cb
I don't know the angles.
How to find the height? Answered by Chris Fisher and Penny Nom. 





Area of a triangle 
20040817 

From Barkie: I'm going into tenth grade and I have a triangle who's sides measure 3ft, 4ft, and 5ft. I need to find the area however I don't know the height, or how to get it. Answered by Chris Fisher. 





Constructing a triangle 
20040808 

From KV: HOW TO CONSTRUCT A TRIANGLE ABC, WHEN
ITS ALTITUDES AD,BE,CF ARE GIVEN Answered by Chris Fisher. 





The law of sines 
20040801 

From Joy: How do you solve this? Do you solve this triangle using the law of sines of the law of cosines? (ASA)
A=120DEG. B=40DEG c=35 cm
I keep getting different answers. Answered by Penny Nom. 





Water in a cone 
20040728 

From A student: A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Answered by Penny Nom. 





The third side of a triangle 
20040728 

From Annette: How do you find the length of a triangle side if you know two sides? Answered by Penny Nom. 





The tangent of theta 
20040710 

From Jacob: P is a point on a unit circle with coordinates(0.6,0.8). Find tan of theta. My book shows me how to do it,"tan of theta=opp./adj.=0.8/0.6=4/3,"and leaves it as that's the answer(4/3).When do we know from a problem to find the angle measure (in this case, the angle measure of theta) and how do we know when to give something like 4/3 without converting it to the angle measure? Answered by Penny Nom. 





The base of a triangle 
20040525 

From Ralph: With a 30 degree angle at the top of a triangle and a height of 15 what is the base? Answered by Penny Nom. 





Some trig expressions 
20040523 

From A student: Prove:
sin A + sin B = 2sin(A+B/2)cos(AB/2)
cos A  cos B = 2sin(A+B/2)sin(AB/2)
cos A + cos B = 2cos(A+B/2)cos(AB/2)
sin A  sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom. 





The perimeter of a triangle 
20040521 

From A student: In a triangle i have the length of a line and it's opposite angle.how can i calculate perimeter?(the angles are not right) Answered by Penny Nom. 





The dimsenions of a room 
20040518 

From Estella: I have a room that is rectangular the area is 159.5 feet, the perimeter is 51 feet what would the dimensions of the room. Answered by Penny Nom. 





Angles of elevation and depression 
20040518 

From Anjum: what is the difference between an angle of elevation and angle of depression? Answered by Penny Nom. 





The height of a triangle 
20040427 

From Danielle: what is the definition of height of a triangle? Answered by Penny Nom. 





A Fibonacci triangle 
20040425 

From Marcelle: Is it possible to construct a triangle with sides that are three consecutive Fibonacci numbers? Answered by Walter Whiteley. 





The sum of angles in a triangle 
20040406 

From A student: How can u prove sum of angles in a triangle equal to 180 degrees? Answered by Penny Nom. 





Trisecting an arbitrary angle 
20040406 

From Joe: Where can I submit my effort on trisecting an arbitrary angle with only a straightedge and a compass? I can do it but I do not have the smarts to prove it.S Answered by Chris Fisher. 





Maximizing the area 
20040327 

From Petey: Please could you tell me why for my coursework (where I have to find the largest area that a fence 1000m long can cover) why I should only test equilateral and isoceles triangles? We were told NOT to do right angled triangles but I was wondering why not?
Answered by Penny Nom. 





Area and perimeter 
20040312 

From Sandy: The rectange has an area of M square units and a perimeter of 2M units. What is the value of x?
The length of the rectange is 3, while the width of the rectange is x1. Answered by Penny Nom. 





Sum of the angles in a pentagon 
20040311 

From Ashish: What is the sum of all the measures of the angles of a Pentagon Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Napoleon's theorem 
20040227 

From David: How do i prove this : For any triangle, if you make 3 equillateral triangles
using the sides of the the original triangle, the central points of the 3
tringles another triangle that is equillateral.z Answered by Chris Fisher and Penny Nom. 





The dimensions of a rectangle 
20040221 

From Jane: A rectangular label has an area of 176cm2 and a perimeter of 54cm. Find the dimensions of the label. Answered by Penny Nom. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Reflex angles 
20040109 

From Sonya: My daughter is searching for examples of reflex angles. We already have the hands of a clock but still need another example. Can you help us. Answered by Chris Fisher. 





The angles in a regular polygon 
20031221 

From Ernie: If i have a measure of one interior angle of a polygon, how can i find the number of sides it has? Answered by Penny Nom. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





The area of a triangle 
20031201 

From A student: Find the Area of Triangle ABC
A(3,2)
B(4,0)
C(0,8) Answered by Penny Nom. 





Area of an equilateral triangle 
20031125 

From Jared: Can you help me understand why the area of a equilateral triangle is the square root of 3 divided by 4 times the lenght of the side squared? Answered by Penny Nom. 





An octagon shaped bed frame 
20031123 

From Trish: My son and I are making an octagon shaped bed frame. We are going nuts trying to figure out what angle to cut the boards to make an outline of an octagon. It seems that the 8 inside angles of the 8 "corners" are 120*, but what is the angle that the 2x6 wood should be cut so that they will angle together to form the outline of the octagon? Answered by Penny Nom. 





A rectangle on a disk 
20031029 

From Arthur: How do I go about solving the following problem: What is the width of the largest rectangle with a length of 16 inches you can cut from a circular piece of cardboard having a 10 inch radius? Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





Points inside a triangle 
20031010 

From Laura:
is there a way to establish, if a given point at coordinates (x,y) is within an area defined by three other sets of coordinates forming a triangle ABC? is T(x,y) within triangle A(x,y)B(x,y)C(x,y) Answered by Chris Fisher. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





A rectangle in a circle 
20030927 

From Abdu: A rectangle ABCD is inscribed in a circle. If the length of AB is 5 and length of BC is 12, what is the area of circle outside the rectanlge ABCD? Answered by Penny Nom. 





Area of a rectangular room 
20030911 

From Kelly: The area of a rectangular room is 238 square feet. The width is 3 feet less than the length. What are the dimensions? Answered by Penny Nom. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.đ The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.đ (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





Cutting some wood 
20030725 

From Betty: My husband is building a six sided wood circle and would like to know the angle to cut the pieces. Answered by Penny Nom. 





A triangle in the complex plane 
20030710 

From Scott: The vertices O and A of an EQUILATERAL triangle OAB in the complex plane are located at the origin and 3 + 3i. Find all possible values for the complex number representing the vertex B. Give the location of B in both polar and cartesian form (to 2.d.p) Answered by Penny Nom. 





Write sin(3x) in terms of sin(x) 
20030505 

From A student: Write sin 2x in terms of sin x Answered by Penny Nom. 





The height of an equilateral triangle 
20030406 

From Rosa: If Each side of an equilateral triangle is 10 m. What is the height? Answered by Penny Nom. 





A triangle and a circle 
20030321 

From Jynks: We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle. Answered by Penny Nom. 





An equilateral triangle 
20030317 

From Shirley: An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible? Answered by Penny Nom. 





Can a square be considered a rectangle? 
20030227 

From Carla:
Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? Answered by Penny Nom. 





A regular polygon 
20030226 

From Melissa: The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? Answered by Penny Nom. 





The area of an isoceles triangle 
20030207 

From A student: I have to find the area of an isoceles triangle with one angle side of 30 degrees, and length of base 5. Could you please help me solve this problem? Answered by Penny Nom. 





Triangle perimeter 
20030130 

From An Aunt:
Hi I'm the aunt of a middle school child. He need help with two problems and I don't understand how to show he how to do them. Can you help me.  How do you find the perimeter for X=4, X=0.7, and X=5/6?
 And an acute triangle that bottom is (3X+1) cm, left side is (X+4) cm and the right is (2X+5)cm.
Can you show me not only the answer but also the steps that you used. Answered by Penny Nom. 





Why quadratic? 
20030121 

From Dan: Why are equations of the form aX^{2} + bX + c =0 call quadratic? The quad indicates 4 but the power is 2. Answered by Penny Nom. 





Radians 
20030116 

From Erikson: I am a student in the 10th grade and attending advanced math at my high school. I was assign to do a report about the unit circle and the radian. But there seems to be no information available about the history of the radian; who first found out about them, which civilizations used it if any. Well, hopefully you'll assist me in this troubling question. Thank you for your kind consideration. Answered by Penny Nom. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





Successive coefficients in Pascal's Triangle 
20021227 

From Quincy: There is a formula connecting any (k+1) successive coefficients in the nth row of the Pascal Triangle with a coefficient in the (n+k)th row. Find this formula Answered by Penny Nom and Walter Whiteley. 





The height of a triangle 
20021129 

From Dean: Could you please tell me the formular for me to calculate the height of a triangle. I have the angles and side lengths. I am trying to calculate the height of an isosceles triangle, does this make a difference from a normal triangle or is the formular the same. Answered by Penny Nom. 





How would you find the length of the chord? 
20021031 

From A draftsperson: If given the length of an arc and the distance from the midpoint of the arc to the midpoint of a chord, how would you find the length of the chord and the radius of the arc. The chords endpoints are the same as the the arcs endpoints. Answered by Penny Nom. 





An isosceles triangle 
20021030 

From Stan: What two different base lengths can an isosceles triangle have with sides on both remaining at 13 inches? How do I show this? Answered by Paul Betts and Peny Nom. 





Is a square a rectangle? 
20021020 

From Nona: Are squares rectangles? Third grade math teacher told a student this was true. Grandmother needs confirmation on this! Answered by Claude Tardif and Harley Weston. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





The area of a triangle 
20020907 

From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom. 





The tangent to a curve and the tangent of an angle 
20020826 

From A teacher: Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)? Answered by Chris Fisher. 





Place six numbers around a triangle 
20020719 

From Monika: I need to place six numbers around a triangle, as such that one number is on each corner, and one number on each side making three numbers in one line, adding up to two hundred exactly. The number I have to use are, 40, 50, 60, 70, 80, 90. I have to use each one once, there for, each number cannot be repeated. Answered by Claude Tardif and Chris Fisher. 





An equilateral triangle 
20020611 

From Sarah: Hi. My name is Sarah. I'm a secondary student taking a Math 30C course by correspondence. The question has two parts.
The first part is: Draw an equilateral triangle XYZ. Draw the altitude from X to YZ. Choose any point P inside the triangle or on the triangle. Draw perpendiculars from P to the sides of the triangle. The Second part is:
Measure the altitude h and the 3 perpendiculars s, t, and u to the nearest mm. Repeat as many time as is necessary until you can state a generalization concerning h, s, t, and u. If you could help me, it would be greatly appreciated. Answered by Penny Nom. 





Successive coefficients in the nth row of Pascal's Triangle 
20020610 

From Tim: There is a formula connecting any (k+1) successive coefficients in the nth row of Pascal's Triangle with a coefficient in the (n+k)th row. find this formula. Answered by Penny Nom. 





Bob swam across a river 
20020522 

From Torri: Bob swam across a river 420 ft wide. A strong current carried him 580ft downstream as he swam. Find x, the distance bob actually swam. Answered by Penny Nom. 





Find the angle measures 
20020518 

From Amanda: In triangle ABC; the measure of angle A is 20 degrees more than twice the angle B. The measure of angle C Is five times angle B. Find the angle measures. Answered by Penny Nom. 





The law of cosines and obtuse angles 
20020509 

From Bryant: The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle. Answered by Penny Nom. 





Moving a triangle 
20020418 

From A student: find the verticles of a triangle after it is translated 2 units to the left and then is reflected across the graph of y=x+2. The original verticles of the triangle are (2,0), (3,2), and (6,2). Answered by Peny Nom. 





Area of a triangle 
20020407 

From Puzzled: What is the surface area of a triangle 13 ft x 13 ft x 18 ft? Answered by Penny Nom. 





Two triangles 
20020403 

From Scott: Consider 2 triangles: Triangle PMB and Triangle PLA. Triangle PLA is contained within Triangle PMB. Side LA is parallel to Side MB. Point L is located on Side PM. Point A is located on Side PB. If the ratio PL:LM = 5, then what is PB:PA ?? Answered by harley Weston. 





Pascal's Triangle 
20020402 

From Brian: It's about (a+b)^{x}. I remember there a triangle with numbers to remember for a faster solution. Can you please teach me? Answered by Penny Nom. 





A triangle in a circle of radius 6 
20020326 

From Marko: In a circle of radius 6, a triangle PQR is drawn having QR = 8 and PQ = 10. Determine the length of PR Answered by Chris Fisher. 





The isosceles triangle of smallest area 
20020308 

From Lettie: can you find the isosceles triangle of smallest area that circumscribes a circle of radius of one? Answered by Walter Whiteley. 





Two circles inscribed in a rectangle 
20020227 

From Amina: Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle. Answered by Penny Nom. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





A rightangled triangle 
20011213 

From Pamela, Jeff, Kayleigh and Jacob: A rightangled triangle has one side that is 8 cm shorter that the hypotenuse. The other side is 1 cm shorter than the hypotenuse. Find the length of the sides. Answered by Penny nom. 





A clap of thunder 
20011115 

From Frustrated Mom: While getting a recipe for the Thanksgiving feast. The teacher was talking on the phone with a friend who lives four miles north of her. She saw a flash of lightning through the window: fifteen seconds later, she heard a clap of thunder. Ten seconds after that she heard the thunder over the phone. Where did the lightning strike in relation to the teacher's house. (There are two possible answers. Sound travels about 1/5 mile per second. Some people say it's not good to be on the phone in a thunderstorm). Answered by Claude Tardif and Penny Nom. 





Prove that the medians of triangle PQR meet in a central point G. 
20011111 

From Jessica: Use a scalene triancle with one point (0,b) on the y axis, another point (2c, 0) on the xaxis and the last point, (2a,0) on the xaxis. Prove that the medians of triangle PQR meet in a central point G. Answered by Penny Nom. 





A circle and triangle overlap 
20011109 

From Tara: A circle and triangle overlap as shown.the area of the circle is three times the area of the triangle.If the common region is removed,then the area of the rest of the circle would be 14 sq cm more than the area of the rest of the triangle.How many sq cm are in the area of the complete triangle. Answered by Penny Nom. 





A circle and a triangle 
20011109 

From Tasha: I have a circle that has an equalateral triangle inscribed in it. The tip of the triangle (B) is at the center of the circle with the other corners (A & C) extending to the sides of the circle. I need to know the equation to find the linear length of AC. I also need to find the cordial length of the circle from point C to A. Answered by Penny Nom. 





Third side of Acute Triangle 
20011109 

From Don: I gave this problem to my children, 9th and 12th grade and they are not(me too!) sure of the answer. I am trying to determine the length of the third side of an acute triangle. I know two of the lengths but I do not know the angles. Is there a proper formula to use to find the length of the third side? Thank you. Answered by Chris Fisher and Penny Nom. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





Where is the fourth point? 
20011024 

From Mike: Four points are placed at random on a piece of paper. Connect the three points of the triangle of the largest area. What is the possibility that the fourth point is in the triangle? Answered by Penny Nom. 





A right angled triangle 
20011023 

From Carissa: How do you : Triangle ABC is rightangled at A. Calculate the length of the third side if b = 3 and c = 6, express the answer as a surd in its simplest form. Answered by Harley Weston. 





Area of a quilt 
20011014 

From Jack:
 how would you find the area of the quilt? which is a square
 how would you fined the area of each square?
Answered by Penny Nom. 





A circle and a triangle 
20011004 

From Christina: The points (3,4), (9.2), and (3,2) define a circle and a triangle.  find the areas of the circle and the triangle. Find the difference between their areas.
 Find the length of a side of a square with the same area as the triangle.
 Find the length of a side of a Square with the same are as the circle.
Answered by Penny Nom. 





The triangle inequality 
20010927 

From A student:
__ __ __
Prove that AX + XB = AB for any X on AB.
Answered by Chris fisher. 





An acute scalene triangle 
20010924 

From Kim: Hi I'm on a missionI'm suppose to have a group of children write up a hypotheses about the altitudes and angle biscetors of the follwing 3 types of triangleequilateral, isosceles and acute scalene triangle. Is there such a thing as a acute scalene triangle and why or why not. Answered by Chris Fisher. 





Similar triangles 
20010908 

From Dave: I am standing on the bank of a river ( whose banks are parallel here) directly opposite a boathouse, B, on the opposite bank. I walk along the bank of the river past a signpost, S, until I reach a point C distant 60 metres from where I started walking. I then walk away from the bank, at right angles to the bank, until I reach a shady tree at D. Attached to teh tree is a sign stating that this spot is 45 metres from the signpost. C is 36 metres beyond S and B and S are in line from D. (a) How far did I walk away from the bank of the river?? (b) Calculate the width of the river? Answered by Penny Nom. 





Bisecting angles 
20010827 

From Monica: Ray QS is the bisector for angle PQR. Find the measure of angle PQS and PQR if the measure of angle SQR is 52 degrees. Answered by Penny Nom. 





Standard angles 
20010805 

From Nagaraj: Why 0^{o} , 30^{o} , 45^{o} , 60^{o} ,and 90^{o} are taken as standard angles in Trigonometry? Why can't we take some other angles as standard angles? Answered by Chris Fisher. 





Radian measure 
20010726 

From Amy: i have to find out what is meant by the radian measure of an angle and compare it to the measure of an angle in degrees. Answered by Harley Weston. 





Rhombus 
20010716 

From William: Calculate the internal angles of a rhombus given measurments of all four sides only. Answered by Walter Whiteley. 





An inequality involving triangles 
20010612 

From Sandra: The triangle inequality guarantees that the sum of the lengths of two sides of a triangle is greater than the length of the third. As a consequence, if x and y are legs of a right triangle, with x less than or equal to y, and z the hypotenuse, then x + y is greater than z, so x is greater than z  y. Under what circumstances will x is greater than 2(z  y) be true? Answered by Chris Fisher and Penny Nom. 





Geometry problems involving triangles 
20010607 

From Sandi: Find the radius of the largest circle contained in a right triangle whose legs are 8 and 15 and hypotenuse is 17. If the right triangle has legs a and b and hypotenuse c, find an expression for the radius of the circle. Answered by Penny Nom. 





Election in Angletown 
20010607 

From Zoe: At the last school election in Angletown 4620 votes were cast. Candidate Acute received 236 more votes than Candidate Obtuse. Candidate Right received 698 votes more than Candidate Acute. Candidate Straight received 256 votes less than Candidate Right. How many votes did each receive? Answered by Penny Nom. 





The angles in a triangle 
20010511 

From Nikki: Find the measure, to the nearest degree, of each angle of a triangle with sides of the given lengths. 26, 35, 40 Answered by Penny Nom. 





Triangles and fractions 
20010427 

From Constance: My name is Constance and I am thirteen years old (I am a student). The question that I am queering about I don't understand why you do ONE HALF x the base x the width WHEN YOU WANT TO FIND the area of a triangle? My second question is if you multiply one half and 10 together why does it come out as 5? Answered by Penny Nom. 





Constructing an equilateral triangle 
20010414 

From Peggy: Please send directions to make an equilateral triangle in plane geometry. I want each student to draw two, cut them out, and place them together to form a Jewish Star. Answered by Penny Nom. 





Squares on a chess board 
20010411 

From Tom: It was once claimed that there are 204 squares on an ordinary chessboard (8sq. x 8sq.) Can you justify this claim? "PLEASE" include pictures. How many rectangles are there on an ordinary chessboard? (8sq. x 8sq.) "PLEASE" include pictures. Answered by Penny Nom. 





The bond angles of a tetrahedral polygon 
20010314 

From Nishi: how do i prove (a simply as possible) why the bond angles of a tetrahedral polygon are 109.5 degrees? *i already have two explanations that i don't understand. one is about "theory of dot products" and "vectors" and a hooklike symbol w/ a cosine, and the other has an incomprhensible diagram w/ difficult notation PLEASE BE SIMPLE! thanks sooo much Answered by Harley Weston. 





The angle of elevation 
20010308 

From Jeffrey: At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun? Answered by Harley Weston. 





How tall is the tree? 
20010302 

From Ronda: a tree's shadow is 42 ft. long. There is a stop sign that is right next to it and it is 18 ft. tall and it's shadow is 12 ft. long. How tall is the tree? Answered by Penny Nom. 





Angles in a polygon 
20010217 

From Joan: How many sides does a polygon have if its smallest interior angle is 120 degrees and each sucessive angle is 5 degrees greater than the predecessor? Answered by Penny Nom. 





The sum of the angles in a polygon 
20010123 

From A student: What is the sum of the measures (interior angles) in an octagon ... heptagon ... decagon. Answered by Penny Nom. 





The hypotenuse of a right triangle 
20010122 

From Phillipe: How do you find the hypotenuse of a right triangle? Answered by Penny Nom. 





A lampost and its shadow 
20001224 

From Laura: A lamppost line EC casts a shadow line AC. A 30 cm ruler line DB has been moved from A so that it's shadow falls just within the shadow of the lamppost.  Suppose the length of the ruler's shadow is 42 cm. What is the slope of the imaginary line AE?
 Suppose the lamppost's shadow is 15 m. long. How tall is the lamppost?
Answered by Penny Nom. 





Is this a right triangle? 
20001208 

From Alicia: How would you setup and answer a problem like these one? Triangle ABC has vertices A(2,2), B(1,2), and C (1,2). Use slopes to determine if the triangle is a right triangle. Answered by Penny Nom. 





The aspect ratio of a rectangle 
20001204 

From Ron Delavigne: The aspect ratio of this rectangle is 4:3. That is A to B is 3. And B to C is 4. If I know the lenght of A to C is 19 inches, how can I find the length of A to B, and B to C. Answered by Penny Nom. 





Triangles and trigonometry 
20001130 

From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston. 





What are adjacent angles that equal 360 called? 
20001122 

From David: I know that supplementary angles add to 180 degrees and that commplementary angles add up to be 90 degrees, but what are adjacent angles that equal 360 degrees called? Answered by Chris Fisher. 





Find the 3D angle 
20001118 

From Jacky: Included is the diagram. I am trying to find out the angle of ABC. Is it possible? How? Answered by Penny Nom. 





Length of a shadow 
20001101 

From Jessy: A man who is six feet tall is walking away from a street light that is fifteen feet tall. How long is the man's shadow when he is ten feet away from the light? Answered by Penny Nom. 





Connecting to a water line 
20001020 

From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom. 





Trigonometry 
20000902 

From david: determine the sum of the angles A,B where 0 <= A , B <= 180 (degrees) sinA + sinB = sqr(3/2) , cosA + cosB = sqr(1/2) Answered by Chris Fisher. 





The angle of rotation 
20000803 

From Jay: I have the following information Given. (X1, Y1) Origional Point (X2, Y2) Origional Point After a Rotation (Xa, Xb) Center of Rotation What formula would I use to figure out the angle the point was rotated? Answered by Chris Fisher and Harley Weston. 





The circumference of a circle 
20000730 

From Not a student: An equalateral triangle is enclosed in a circle. The three corners touch the edges of the circle. One side of the triangle is 12. What is the circumference of the circle? Answered by Penny Nom. 





A semicircle and a triangle 
20000728 

From Ben: A semicircle and an isosceles triangle ABC have the same base AB and the same area. The equal angles in the triangle are BAC and CAB. I have to find the value of each of these angles. Answered by Harley Weston. 





Rectangles and algebra 
20000613 

From Kirstin: A rectangle's length is 4 more than twice its width. The area of the rectangle is 336m squared. What is its length? Answered by Paul Betts and Penny Nom. 





Projecting a line segment onto a plane 
20000608 

From Monica: What is the measure of the angle determined by a 14 inch segment and its projection into a plane if the length,in inches, of the projection into the plane is 7 inches? Answered by Penny Nom. 





A centroid problem 
20000602 

From Kerstin: An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle. Answered by Harley Weston. 





Adjacent Angles 
20000521 

From Katherine Keys: Can a straight angle be an adjacent angle to another angle? Answered by Chris Fisher. 





The pythagorean theorem 
20000519 

From Lauren Fitzgerald: how do you find the length of th hipotnuse( or however you spell that word). i understand you have to add the two sides. but when i do add i always end up with this way off answer. i donot understand at all. Answered by Paul Betts. 





Supplementary angles 
20000509 

From Suzanne: We know that: Supplementary angles are two angles whose sum equals 180 degrees and complementary angles are two angles whose sum equals 90 degrees. Are supplementary and complementary angles necessarily adjacent? or can they be nonadjacent? Answered by Chris Fisher. 





sin(7pi/12) 
20000504 

From Kristel: What is the exact value of sin 7pi/12? Answered by Chris Fisher and Paul Betts. 





Monica's geometry problem 
20000427 

From Monica: Given: ABCD is a square; AX is perpendicular to BY Prove: Angle 1 is congruent to Angle 3 Answered by Chris Fisher. 





The area of a triangle using calculus 
20000415 

From Todd Bowie: Hi, I am not a student but am reviewing calculus for an upcoming interview. I would like to know how to derive the area of a triangle using calculus. Thanks! Answered by Patrick Maidorn. 





Magic triangles 
20000411 

From Sandy: My tutoring student brought math homework today in the form of a "magic triangle". There are three spaces along each side for missing numbers. The sums of the numbers along each of the 3 sides should be the same. Use the numbers 4 through 9. Don't use any number more than once. The sum of the numbers on each side should be 20. What is the logic behind solving a problem of this kind? Answered by Claude Tardif and Harley Weston. 





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





Why a Right angle? 
20000403 

From Joseph Mizerek: I was wondering why a 90 degree angle is called a Right angle. I mean why isn't called a left angle. Answered by Haragauri Gupta. 





Reflex angles 
20000322 

From D. Reed: What is the name of an angle that exceeds 180 degrees? Answered by Penny Nom. 





An equilateral triangle in a circle 
20000311 

From Michael Setlik: An equilateral triangle is drawn within a circle such that all three points of the triangle just touch the inside of the circle. Given the diameter of the cicle as six inches what is the length of the sides of the triangle? Answered by Harley Weston. 





Angle of Intersection of Two Lines 
20000302 

From Veronica Patterson: I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1theta sub2)= ((m sub2 m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Answered by Harley Weston. 





Proportionality in a triangle 
20000301 

From Courtney Smith: I would appreciate assistance with the following problem In triangle ABC,segment MN divides sides(segment)AC and (segment)AB proportionally. If the coordinates are A(3,7),M(0,10) and N(8,22) and if AM:MC = 3:1, find the coordinates of B and C. Answered by Penny Nom. 





Building a pyramid 
20000226 

From Francis X. Hines Jr.: I am presently trying to build a pyramid. I can understand that the base has 90 degree angles on the first plane which is the outline of the square that makes up the floor. As close as I can figure the slope of each wall face is 35 degrees or 35.7 to be exact if I am correct by using 360 as the total of the three interior angles.Now , I run into a compound angle where the corners meet what would be the angle created by the two 35 degree angles that would allow for the 90 degree edge to continue. Because I'm working in three dimensions I also need to be sure that my math would be correct when I substract 35 from 90 to aquire the angle of the narrow edge as to allow for a 90 degree surface to be present ..to allow for another level to be added with only the base line being shortened. I hope you can understand what it is that I'm asking assistance with.I would greatly appericate your help. Answered by Chris Fisher. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





A triangle and a circle 
20000223 

From wendy: If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle? I am having trouble with altitude. Answered by Penny Nom. 





Is a square a rectangle? 
20000215 

From Jaireh: This is something that aroused a debate in class: A rectangle was defined as a parallelogram with 4 right angles. A square was defined as a parallelogram with 4 congruent sides and 4 right angles. I need written and conclusive proof that some rectangles can or cannot be squares. I tried insisting that some of them can.. but without proof nobody will listen. Answered by Walter Whiteley. 





Euclidean Math puzzle 
20000124 

From Margaret Matthews:
(Check out this website: Simeon's Triangle Puzzle ) I have tried to figure out how this could be, because everything I know about it tells me it can't be. However, I can't seem to make it NOT work. Two right angle triangles. They are each cut up into four identical pieces. In the first, all the pieces fit together so that there are NO empty spaces; in the second, presumed to be identical in size to the first, the pieces are slightly rearranged, and now, there IS a space in the triangle. Answered by Patrick Maidorn and Claude Tardif. 





Three dimensional rectangle 
20000111 

From Dennis Murphy: I would like to find out the name of a Three dimensional rectangle. Answered by Harley Weston. 





Angles 
20000106 

From Rayna: I am doing a presentation report on angles which has to be fun and entertaining as well as educational. I am having problems locating resources on angles that give me ideas of fun entertaining projects. My lecture is to be about 20 minutes long infront of a class of 11th and 12th graders. Please Help if you can. Answered by Claude Tardif and Walter Whiteley. 





Multinomial coefficients 
19991203 

From Suraj Das: Is there a formula for the expansion of (a+b+c) to the nth power? Does it have to do with Pascal's triangle? Answered by Penny Nom. 





An area problem 
19991129 

From Vicky Birch: The length of a rectangle is three times it's breadth. If the length were 6 meters less, and the breadth were 6 meters more, the rectangle would be a square. Make a mathematical model and solve the resulting equation to find the breadth of the original rectangle. What is the area of the square? Answered by Penny Nom. 





Area of a quadrilateral 
19991119 

From Zane Cram: I need the formula to calculate the area of an irregular sided rectangle. Each side has a different measurement or length. Answered by Walter Whiteley. 





Transforming a triangle 
19991102 

From Wilder Maldonado: The height, H, of a triangle is increased by a lenth M, How much must be subtracted from the corresponding base,b, so that the area of the new triangle is onehalf that of the original triangle. Answered by Penny Nom. 





Isosceles triangles 
19991012 

From Amber: In defining the types of triangles, our class was stumped by a question asked by one of the student. Maybe you could help. The definition of an equilateral triangle is a triangle with three congruent sides. The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides. The question is, if an isosceles triangle only requires at Least two of the sides to be congruent, could an equilateral triangle be called an isosceles triangle? Answered by Penny Nom, Walter Whiteley and Chris Fisher. 





Two 12sided polygons 
19990925 

From Kelly Boulton: Two 12sided polygons are similar. A side of the larger polygon is 3 times as long as the corresponding side of the smaller polygon. wHAT IS the ratio of the area of the larger polygon to the area of the smaller polygon. Answered by Walter Whiteley. 





Degrees and triangles 
19990909 

From Sandra Mills: Are there any triangles which are not 180 degrees? I am also in need of information on the history of degree measure for an angle. Answered by Walter Whiteley. 





A Trigonometry Question 
19990828 

From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin^{2}X + 2 SinX CosX  1= 0 Answered by Harley Weston. 





Sin 4A 
19990622 

From Ryan Cochrane: If sinA = 4/5, and A is a first quadrant angle, find sin4A Answered by Harley Weston. 





Girth 
19990526 

From Carolyn Bulkley: I am trying to explain to my son (who is in the 8th grade) how to figure girth. I'm afraid I have just confused him. Is there a simply formula to figure the girth of a box. for example: I have a box that is 27" L X 22" W X 21" H. Answered by Penny Nom. 





An equilateral triangle on a square 
19990426 

From Ed: My Grade 8 class and I were discussing the solution to the following problem: What is the area of the largest equilateral triangle that can be drawn on a 5 cm square. We used 5 cm as the base of our triangle and then drew the other two legs of 5 cm each to make the equilateral triangle. We then drew an altitude from the upper vertex to the base of the triangle. Using the law of Pythagoras with side a of 2.5 and side c of 5 we calculated side b to be 4.3 cm (the altitude). Therefore the area of the triangle would be 5 x 4.3 divided by 2 or 10.75 square cm. The answer key to this resource says I am wrong. What do you think? Have we interpreted the question incorrectly? Answered by Chris Fisher and Harley Weston. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Area of a triangle from vertex coordinates 
19990421 

From Mark Tyler: I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too. I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula: A = abs((x1x2)*(y1y3)(y1y2)*(x1x3)) for triangle (x1,y1)(x2,y2)(x3,y3) I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long. Regardless, it may be fun for the kids, even if it's not on the curriculum. Answered by Walter Whitley. 





Universal Area 
19990408 

From Karen Richardson: I need a formula for area that works for a square, a rectangle, a parallelogram, a trapezoid, and a triangle. Answered by Jack LeSage, Chris Fisher and Harley Weston. 





Angles in Polygons 
19990121 

From Jen:
 How do u find the interior angles of a pentagon when you are given 4 of the angles and you need to find the fifth?
 If you are given the measure of each exterior angle of a regular polygon, how do you figure out how many sides the polygon has?
 i need all information on polygons and how to find their angles!!!
Answered by Jack LeSage. 





The area of a triangle 
19981226 

From Elysia: How do you figure the square inches of a triangle? Answered by Harley Weston. 





Two sides and a bisectrix. 
19981111 

From Victor Grinshtein: I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler. Answered by Chris Fisher. 





Triangular Numbers 
19981030 

From Matt: i would like to know about triangular numbers and it history i would also like to know about the history of prime numbers thank you Answered by Chris Fisher. 





Complementary and Supplementary Angles 
19981021 

From Christina Saunders: I am in 9th grade and my math teacher wanted us to find out why complimentary angles are called complimentary and why supplimentary angles are called supplimentary. I have looked everywhere and asked numerous people, but I have yet to find an answer. My math teacher said it had something to do with trigonometry. Do you have an answer for me? Answered by Chris Fisher and Penny Nom. 





Concurrent Lines in a Triangle 
19980810 

From Chris Woolf: The question is Name four types of concurrent lines, rays, or segments that are associated with triangles. Answered by Chris Fisher. 





Area and Volume 
19980728 

From James Pulver: I am going into 12th grade and am practicing for the SAT II. I have come across a problem that I cannot solve. It states that the front, side , and bottom faces of a retangular solid have areas of 24 square centimeters, 8 square centimeters, and 3 square centimeters, respectively. What is the volume of the solid. I need to know how to solve similar problems so is there a formula to go from area to volume? Answered by Jack LeSage. 





Area of a Triangle. 
19980305 

From Amanda: How do you figure out the area of a triangle? You already have the perimeter and height Answered by Penny Nom. 





The origin of angles 
19980224 

From Marc Poulin: I'm currently teaching angles to students in grade 10 and I've been asked what's the origin of the terms degrees, radians and gradians. I know that the radians come from the sexagesimal numerical system of the Babylonians but my kids wanted to know dates and persons who would have brought these terms first. Answered by Harley Weston. 





The sum of the angles of a triangle is 180 degrees 
19980219 

From Quin Liu: How do you prove that the sum of the angles of a triangle is 180 degrees? Is there a proof? what is it? Answered by Chris Fisher. 





Area of a triangle. 
19980201 

From Jodi Blucher: Is there a formula for the area of an equilateral triangle knowing the length of the sides? Answered by Chris Fisher and Harley Weston. 





Trigonometric functions 
19971221 

From Calvin Cheng: My name is Calvin and I have a year 12 question for you to help me with. From a point S, the angle of elevation of the top of a tower due north of it is 20 degrees. From R, due east of the tower, the angle of elevation is 18 degrees. S and R are 100m apart. Find the height of the tower. Answered by Harley Weston. 





Pythagorean Triples. 
19971204 

From Shameq Sayeed: I've got a couple of problems which I hope you'll be able to solve for me. I'm investigating pythagorean triples, and I have found a trend for the triples themselves, and thus have been able to form a general equation, i.e. a=2x+1, b=2x^2+2x, and c=b+1. Now, I sure this equation works, because I've tried it out and have come up with triples that adhere to a^2 + b^2 = c^2. But I was wondering WHY c=b+1. Is it possible to have c=b+2, and if not why not? THAT is the first problem. Answered by Chris Fisher. 





Shimin's Geometry Problem 
19971202 

From Ong Shimin: ABCD is a rectangle. X and Y are the midpoints of BC and CD respectively. W is a point on AB such that AW : WB = 2 : 1. Z is a point on AD such that AZ : ZD = 2 : 1. WY intersects XZ at O. If the area of triangle WOZ is 84 centimeters squared, find the area of triangle XOY. Answered by Chris Fisher. 





A geometry problem 
19971120 

From Herman: When produced, two equal chords AB and CD of a circle meet at P in an angle of 24 degrees. If H is the midpoint of AB and K is the midpoint of CD, calculate the size of angle HKD. Answered by Penny Nom. 





A Geometry Problem 
19970918 

From Rebecca Henry: A circle is centered at the vertex of the right angle of an isosceles triangle. The cirlce passes through both trisection points of the hypotenuse of the triangle. If the length of a radius of the circle is 10, find the area of the triangle. Answered by Chris Fisher Harley Weston. 





Finding the Mine 
19970623 

From Billy Law: Tom is gold prospector. On his last trip out from town, he headed 35 degree South of West to a lake where he had lunch. The lake was 24 km out of Town. He then headed due East for 35 km before Doubling back on bearing of 15 degree South of west for 20 km to reach his mine. By converting to Cartesian coordinate before doing vector additions do the following: a) Calculate the position of the mine from town in term of a distance and a direction. ... Answered by Harley Weston. 





The angle between two tangents. 
19970609 

From Felix Ho: Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)4x6y+9=0. If the angle between the tangents is m, fine the value of tan(m). P.S. (x)(x)=square x Answered by Harley Weston. 





The Area of a Trapezoid. 
19970507 

From Mary George: I am doing the area of trapezoids and mixed polygons and I was wondering if you can help me figure out this problem. A line segment drawn parallel to a leg of a right triangle divides the other leg into segments of 3cm and 6 cm and the hypotenuse into segments of 5cm and 10 cm. The two figures formed are a triangle and a trapezoid. Find the area of each. I would appreciate if you would email me back the solution. Answered by Harley Weston. 

