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Complementary angles 2017-09-15
From SM:
The measure of angle A is 60 degrees more than its complement. Find the measure of angle A.
Answered by Penny Nom.
Squares and rectangles 2017-07-15
From Tront:
So, there's a general rule that all squares are rectangles but not all rectangles are squares. Im trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole.
Answered by Penny Nom.
An angle and its complement 2017-01-10
From Ysa:
If the measure of an angle is twice the measure of its complement, what is the measure of the angle?
Answered by Penny Nom.
Hexagonal pyramid bevel angles 2016-09-30
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 number of sides of a polygon 2016-07-23
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 2016-07-17
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 2016-06-09
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 2016-05-21
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.
External and interior angles of a regular polygon 2016-04-19
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.
Angles 2016-03-12
From Laurynn:
What are angles in general (please include the 'angle of incline')

Thank you
Laurynn

Answered by Penny Nom.
The sum of the angles of a triangle 2016-02-24
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 2016-02-17
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.
Consecutive angles of a parallelogram 2016-01-28
From Hanna:
The consecutive angles of a parallelogram measures
Answered by Penny Nom.
The angles of a triangle 2015-12-17
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 measure of an angle in terms of its complement 2015-11-22
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 shadow 2015-08-01
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.
An octagonal frame around a pool 2015-05-17
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.
Cutting a hexagon with a sliding miter saw 2014-11-23
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 2014-10-14
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.
Interior angles in a parallelogram 2014-08-30
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.
A barge of triangular cross section 2014-08-18
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 length of a shadow 2014-05-09
From vijay:
A girl of height 80 cm is running away from the base of a lamp-post 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.
Two cones 2014-04-09
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.
Shadows of a father and son 2014-04-02
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.
A triangle has angels in the extended ratio of 2:5:8 2014-02-06
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.
Constructing a triangle 2013-08-22
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 2013-08-17
From Mattie:
The dimensions of a rectangular-shaped 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.
A triangle construction 2013-07-27
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.
A kennel for a beagle 2013-06-03
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.
A triangle and an incircle 2013-05-09
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 2013-05-06
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.
Trigonometry 2013-03-23
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.
Three right triangles 2012-07-26
From Jora:
I am having a lot of difficulties with this question.

Name: Jora
Subject: Math
Who are you: Student

Answered by Chris Fisher.
An octagonal sandbox around a pool 2012-06-12
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.
Squares and triangles 2011-12-06
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 theta-3=1 2011-12-02
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 theta-3=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 right angled triangle 2011-10-31
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.
Building a custom range hood 2011-10-08
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.
Dividing a polygon into triangles 2011-04-16
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.
The interior angles of a pentagon 2011-03-10
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.
Triangles with perimeter 16 cm 2011-02-22
From Chong:
How many triangles (up yo congruence) with perimeter 16 cm and whose lengths of its side are integers?
Answered by Chris Fisher.
Calibrating a conical tank 2011-02-05
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.
The height of a lamp 2011-01-13
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.
Draw a figure with 16 triangles using only 6 line segements 2010-12-16
From Jill:
How can you draw a figure with 16 triangles using only 6 line segements?
Answered by Stephen La Rocque.
The angles in an m-gon and genrealizations 2010-10-16
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.
A spaceship playhouse 2010-07-26
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 2010-07-09
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 2010-06-24
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.
An angle in a triangle 2010-05-06
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 2010-05-04
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.
An irregular octagon 2010-03-09
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.
How many triangles...? 2010-02-22
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 2010-02-19
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.
Triangles on a base of 2.4 meters 2009-12-26
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.
Polygons, diagonals and the sum of the measures of the angles 2009-12-18
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 line through D(-4, 0) and E(2, 6) 2009-11-16
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 three angles of a triangle 2009-10-13
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.
Two rectangles 2009-10-08
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 2009-10-05
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 paper towel roll 2009-08-19
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.
How can I trisect an angle? 2009-07-27
From Nazrul:
How can I trisect an angle?
Answered by Robert Dawson.
The position of the fulcrum 2009-05-23
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.
The sum of the angles of a triangle 2009-05-18
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 2009-05-16
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.
The hypotenuse of a right angled triangle 2009-05-11
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.
The interior angles of a pentagon 2009-04-20
From Mary:
If four interior angles of a five-sided figure pentagon measure 100 degrees each, what will the fifth angle measure?
Answered by Harley Weston.
Two similar rectangles 2009-04-19
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 angles of a triangle 2009-03-11
From Marissa:
The angles in a triangle measure 7x-1, 18x+2, and 5x+10. Determine whether the triangle is acute, obtuse, or right. State your reasons clearly.
Answered by Robert Dawson.
Triangles within triangles 2009-02-24
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 2009-02-24
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.
Forming an arc with 2 inch steel 2009-02-11
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 30-60-90 triangle 2009-02-03
From Inez:
If you have a 30-60-90 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 ratio of the measures of the three angles of a triangle 2009-01-18
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.
A stack of rectangles 2009-01-11
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 flat-topped pyramid 2009-01-10
From Tom:
I am planning to build an open ended, flat-topped 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 2009-01-08
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.
Pouring angles for a crucible 2008-12-20
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.
The volume of a feed hopper 2008-12-18
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.
3 equidistant points 2008-12-01
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 midpoint o a line segment 2008-11-15
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 2008-11-13
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 2008-11-10
From Anna:
<A and <B are supplementary angles. Twice the measure of <B is one-fourth the measure of <A. Find the measure of both angles.
Answered by Penny Nom.
A flagpole and a yardstick 2008-11-07
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 angles of a triangle 2008-10-31
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 2008-10-27
From Meagan:
Here is my problem: Three congruent (non-square) 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.
Octagon angles 2008-10-06
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.
Supplementary angles 2008-09-11
From Shanaz:
Find an angle such that 3 times its supplement equals 450.
Answered by Penny Nom.
Number of angles formed by rays 2008-08-29
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.
Angles in an octagon 2008-08-26
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.
Joining vertices in a polygon 2008-08-18
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.
Similar Triangles Given a Median 2008-08-17
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 2008-08-12
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.
Angles in a regular tetrahedron 2008-08-07
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.
The angle between two faces of a pyramid 2008-08-06
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 2008-08-04
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.
Hexadecagon 2008-07-09
From Dave:
I would like to know at what length and angle I would cut wood to make a Hexadecagon.
Answered by Penny Nom.
Fit 7 different rectangles on grid paper 2008-07-02
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 2008-06-26
From evelina:
how many sides has a regular polygon if the measures of the exterior angle is given
Answered by Walter Whiteley.
sin(2x)/sin(3x) 2008-06-19
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.
The angles of a parallelogram 2008-06-11
From light:
ABCD is a parallelogram. If angle A. = (4x=17)degrees and angle B. = (3x-5)degrees , what is angle c?
Answered by Penny Nom.
The two acute angles in a right triangle 2008-06-05
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 18-sided polygon 2008-06-04
From Alfred:
How do I find the sum of the interior angles of an 18-sided polygon?
Answered by Janice Cotcher.
The angles of an irregular pentagon 2008-05-20
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.
The Pythagorean theorem with triangles rather than squares 2008-04-29
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.
Side lengths and angles in a regular octagon 2008-04-09
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.
A fish tank in the shape of an irregular pentagon 2008-03-29
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.
Similar triangles 2008-03-26
From Nisha:
In triangle ABC, LM is parallel to AB. If AL=x-3,AC=2x,BM=x-2,BC=2x=3. Find x
Answered by Penny Nom.
A word problem about a triangle 2008-03-23
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.
Angles subtended by the same arc 2008-03-23
From Reid:
Prove that two inscribed angles subtended by the same arc are equal.
Answered by Stephen La Rocque.
A 6 pointed star 2008-03-04
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 2008-03-01
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.
Two right triangles 2008-02-18
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.
A flagpole and a statue 2008-02-09
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 interior angles of a parallelogram 2008-01-29
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 2008-01-28
From steffie:
How do you calculate the interior angle sof a parallelogram?
Answered by Penny Nom.
The three angles of a triangle 2008-01-21
From val:
two angle in a triangle equal 120 degree. what is the measure of the third angle?
Answered by Penny Nom.
The angles of a triangle given the three sides 2008-01-17
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.
Forces on an inclined plane 2008-01-10
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.
Lining up coins visually using geometry and trigonometry 2007-12-31
From Jessica:
a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a half-dollar 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; half-dollar, 1205.
b) How should the coins be placed, if the distance between the dime and the half-dollar 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.
How many triangles can be formed? 2007-12-21
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.
Smallest cone containing a 4cm radius inscribed sphere 2007-12-19
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.
Finding all the angles 2007-12-13
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.
What angle should he turn? 2007-12-01
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.
Related Rates (streetlamp and shadow) 2007-11-09
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 2007-11-08
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.
Two mirrors 2007-10-24
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? 2007-10-24
From Maria:
Given a six by six square, how rectangles are there in the square?
Answered by Stephen La Rocque.
Surface area of an open-ended cone 2007-10-16
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.
The angles in a polygon 2007-10-11
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(n-2). If there is any easier methods to prove the problem, please write as well.
Answered by Stephen La Rocque.
Finding equations, intersection point of two lines at right angles 2007-09-22
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 co-ordinates of D.
Answered by Stephen La Rocque.
Composite angles 2007-09-13
From Gilbert:
what is a composite angle? please help
Answered by Stephen La Rocque.
Similar triangles 2007-08-29
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 2007-08-25
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.
Finding the radius of an inscribed circle 2007-07-05
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.
Volume in a triangular water trough 2007-06-24
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 2007-06-21
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.
How can I find out how many sides there are? 2007-04-23
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.
Interior and exterior angles 2007-04-02
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. 2007-03-28
From Brittney:
The smallest angle in a triangle is one-third 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 height of a pole 2007-03-22
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.
Similar triangles 2007-02-21
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.
The interior angles of a parallelogram 2007-02-07
From jenniffeir:
Can a parallelogram have two 45 degree angles and two 75 degree angles?
Answered by Haley Ess.
Angle of elevation 2007-02-05
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.
Height of a right triangle? 2007-01-29
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.
In the shadow of a building 2007-01-11
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.
Are all rectangles trapezoids? 2007-01-05
From Sarah:
Are all rectangles trapezoids?
Answered by Chris Fisher.
How do the perimeters of the two pentagons compare? 2007-01-02
From Robert:
If the area of one pentagon is eighty-one times the area of another pentagon, how do the perimeters of the two pentagons compare?
Answered by Penny Nom.
An octagonal birdhouse 2006-12-30
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 sum of the angles in a triangle 2006-12-12
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 building 2006-11-19
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.
An equilateral triangle has been wedged in between two circles. 2006-09-22
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 2 sides of a triangle 2006-09-15
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.

How high (in feet) is the mountain? 2006-08-29
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 2006-08-17
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 2006-08-13
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 2006-08-12
From Erin:
Water runs into a conical tank at the rate of 9ft3/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 r2 h).
Answered by Penny Nom.
Designing a garage 2006-06-08
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.
What is the measure of the interior angles of a decagon? 2006-05-10
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.
Finding the supplementary angles 2006-04-22
From Kendra:
Angles ABC and DBA are supplementary. If m
Answered by Stephen La Rocque.
Solve the equation cos x = sin 20 where x is acute. 2006-03-26
From Elle:
Solve the equation cos x = sin 20 where x is acute.
Answered by Stephen La Rocque.
The volume of water in a cone 2006-03-21
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.
Heights and shadows 2006-03-06
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.
How do you find the angles in a triangle? 2006-01-27
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.
Subdividing a polygon into triangles 2006-01-26
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 2006-01-25
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 2006-01-25
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 2006-01-23
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 2006-01-22
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.
Interior and external angles of a polygon 2006-01-17
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 sum of the angels in a triangle 2005-11-25
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 2005-11-25
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.
The height of a tower 2005-11-08
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 2005-11-04
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 sum of the measures of the angles of a decagon? 2005-10-15
From Dianna:
What is the sum of the measures of the angles of a decagon?
Answered by Penny Nom.
A 30-60-90 triangle 2005-09-11
From Gary:
I have the length of only 1 side of triangle with angles of 30-60-90 degrees. How can I find the length of the other 2 sides?
Answered by Penny Nom.
Is 360 Really the correct value? 2005-08-15
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.
The centroid of a triangle 2005-04-07
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.
Each interior angle of a particular polygon is an obtuse angle... 2005-02-22
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 2005-01-22
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.
Is a square a rectangle? 2004-11-21
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 2004-11-16
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.
Solving triangles 2004-10-30
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.
Two gears 2004-10-14
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.
Supplementary angles 2004-09-23
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.
Fabricating with pipe 2004-09-19
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.
Water in a cone 2004-07-28
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.
A Fibonacci triangle 2004-04-25
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 2004-04-06
From A student:
How can u prove sum of angles in a triangle equal to 180 degrees?
Answered by Penny Nom.
Sum of the angles in a pentagon 2004-03-11
From Ashish:
What is the sum of all the measures of the angles of a Pentagon
Answered by Penny Nom.
A geometry problem 2004-03-04
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 2004-02-27
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.
Sin(3x), cos(3x) and tan(3x) 2004-01-28
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 cos4x- sin4x is the same as cos2x. Is cos8x-sin8x = cos2x also true? Thank you.s
Answered by Chris Fisher.
Reflex angles 2004-01-09
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 2003-12-21
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 2003-12-02
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 2003-12-01
From A student:
Find the Area of Triangle ABC
A(-3,2)
B(4,0)
C(0,8)

Answered by Penny Nom.
An octagon shaped bed frame 2003-11-23
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.
Squares in a rectangle 2003-10-21
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.
Two chords 2003-10-07
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.
Water in a cone 2003-08-12
From Adrienne:

Water is poured into a tank in the shape of an inverted right circular cone.ð 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.ð (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 r2 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 2003-07-25
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.
An equilateral triangle 2003-03-17
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? 2003-02-27
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 2003-02-26
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 2003-02-07
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.
Radians 2003-01-16
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.
A Circle is evenly divided into six equal triangles 2002-09-16
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 2002-09-07
From Phill:
How do you find the area of a equilateral and other triangles?
Answered by Penny Nom.
Find the angle measures 2002-05-18
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 2002-05-09
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.
Two triangles 2002-04-03
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.
Two circles inscribed in a rectangle 2002-02-27
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.
Similar triangles 2001-09-08
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 2001-08-27
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 2001-08-05
From Nagaraj:
Why 0o , 30o , 45o , 60o ,and 90o are taken as standard angles in Trigonometry? Why can't we take some other angles as standard angles?
Answered by Chris Fisher.
Radian measure 2001-07-26
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 2001-07-16
From William:
Calculate the internal angles of a rhombus given measurments of all four sides only.
Answered by Walter Whiteley.
An inequality involving triangles 2001-06-12
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 2001-06-07
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.
The angles in a triangle 2001-05-11
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 2001-04-27
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.
Squares on a chess board 2001-04-11
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 2001-03-14
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 hook-like symbol w/ a cosine, and the other has an incomprhensible diagram w/ difficult notation- PLEASE BE SIMPLE! thanks sooo much
Answered by Harley Weston.
How tall is the tree? 2001-03-02
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 2001-02-17
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 2001-01-23
From A student:
What is the sum of the measures (interior angles) in an octagon ... heptagon ... decagon.
Answered by Penny Nom.
A lampost and its shadow 2000-12-24
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.
  1. Suppose the length of the ruler's shadow is 42 cm. What is the slope of the imaginary line AE?

  2. Suppose the lamppost's shadow is 15 m. long. How tall is the lamppost?

Answered by Penny Nom.
Is this a right triangle? 2000-12-08
From Alicia:
How would you set-up 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.
Triangles and trigonometry 2000-11-30
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? 2000-11-22
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.
Length of a shadow 2000-11-01
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 2000-10-20
From Vanja:
My question is...A house is to be connected to a new water main that runs along the line y=2/3x-1. 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 2000-09-02
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.
Rectangles and algebra 2000-06-13
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 2000-06-08
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 2000-06-02
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 2000-05-21
From Katherine Keys :
Can a straight angle be an adjacent angle to another angle?
Answered by Chris Fisher.
Supplementary angles 2000-05-09
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 non-adjacent?
Answered by Chris Fisher.
sin(7pi/12) 2000-05-04
From Kristel:
What is the exact value of sin 7pi/12?
Answered by Chris Fisher and Paul Betts.
Monica's geometry problem 2000-04-27
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 side length ratios of some triangles 2000-04-04
From Alexis Lockwood:
I am doing a project for my Math 30B class regarding the side length ratios of 45-45-90 degree and 30-60-90 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? 2000-04-03
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 2000-03-22
From D. Reed:
What is the name of an angle that exceeds 180 degrees?
Answered by Penny Nom.
Building a pyramid 2000-02-26
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.
Angles 2000-01-06
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.
Area of a quadrilateral 1999-11-19
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.
Isosceles triangles 1999-10-12
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 12-sided polygons 1999-09-25
From Kelly Boulton:
Two 12-sided 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 1999-09-09
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 ladder problem 1999-04-22
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.

Angles in Polygons 1999-01-21
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.
Complementary and Supplementary Angles 1998-10-21
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.
The origin of angles 1998-02-24
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 1998-02-19
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.
Trigonometric functions 1997-12-21
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.

Shimin's Geometry Problem 1997-12-02
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 1997-11-20
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 mid-point of AB and K is the mid-point of CD, calculate the size of angle HKD.
Answered by Penny Nom.
Triangles, The Pythagorean Theorem and Pizzas. 1997-02-23
From Sherryle Mathis:
I am a graduating senior presently teaching geometry as part of my student teaching. I will do my CUP on Right Triangles and Pythagorean theorem. I am looking for a fun activity as part of my unit plan.
Answered by Walter Whiteley.
Sides in a Regular Polygon 1996-12-06
From Rick Moss:
If you are given the measure of each interior angle (162 degrees) of a regular polygon. How many sides does the polygon have?
Answered by Penny Nom.
Height of a Hotel 1996-11-07
From Irene:
"Irene" is to determine the # of floors in a hotel 500 feet up the street. Irene is on the 10th floor of an office building and can measure the angle of elevation to the top of the hotel, 57 degrees. Her view of the entire building is obstructed. If the street rises at an angle of 8 degrees from the office building to the hotel and the average distance between floors is 11 feet, how many floors are on the hotel?
Answered by Penny Nom.
Why is a circle divided into 360 degrees? 1996-09-30
From Kurtis Kredo:
I was recently wondering why a circle has been divided in to 360 degrees. When I asked my physics teacher he could not think of an answer. His guess is that it probably has to do with people long ago using the base 6 number system. I have a small inkling that it has to do with easy conversion or usage with radians or grads.
Answered by Chris Fisher.
Un polyedre ayant comme face 20 triangles 2000-08-02
From Sonia:
J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux.
Answered by Chris Fisher.
Maths 1999-01-11
From Stephane Roissard:
Soit ABC un triangle dans lequel les trois médianes sont de meme longueur. Montrer que ce triangle est quilatéral.
Answered by Jack LeSage.
Question de trigonométrie 1997-12-11
From Jean-Pierre Quesnel:
Je suis dans le désert et je parcours 1000 km à partir du point "A" jusqu'au point "B". Si je reviens au point "A" et fais une rotation de 8 degrés en faisant un autre 1000 km, quelle sera la distance en km entre les points "B" et "C".
Answered by Diane Hanson et Penny Nom.
 
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