







The height of a building 
20190405 

From Hayley: A young man is 36 meters away from a building and looking at a bird sitting on top of the building. The man knows he is 85 meters away from the bird. How tall is the building? Answered by Penny Nom. 





How far is the boat from the harbour? 
20161006 

From Karabo: a boat sails 30 km due east from a harbour. Then it sails 40 km due north. How far is it from the harbour? Answered by Penny Nom. 





A puzzle embedded in a table top 
20160513 

From Aaron: I want to make a table with a puzzle embedded in it. The table top would be a
36" circle and the puzzle is 20"x27" I'm thinking that it's not going to fit,
but not sure. Any help would be appreciated.
Thanks,
Aaron Answered by Penny Nom. 





The diagonal of a 10 acre square 
20160411 

From Derrick: I own 100 acre square of land. I want to run from farthest corner of property to farthest corner, Diagonally. How many miles would I have traveled? 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. 





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. 





The area of a quadrilateral 
20131221 

From khushboo: Find the area of quadrilateral pqrs in which
angle QPS=90°,PQ=12cm, PS=9cm, QR=8cm and SR=17cm.
(Hint: PQRS has two parts) 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. 





A circle and a chord 
20120211 

From Sophia: The diagram shows a circle with a chord that is 10cm long. The middle of the chord is 12cm from the centre of the circle. Calculate the radius.
Chord length is 10cm.
The distance from the centre to chord is 12 cm. Answered by Penny Nom. 





The perimeter of a figure 
20110427 

From syed: Hello I'm Syed from Bangladesh.
Please help me out! It is killing me.
The question is=2C find the perimeter of the figure. I can't find the perimeter.
I am enclosing the figure as an attachment. 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. 





How far is it from the control tower? 
20110411 

From Varun: An aircraft is vertically above a point which is 10 kms west and 5 kms north of a control tower. if the aircraft is 4000 mts above the ground,how far is it from the control tower? Answered by Penny Nom. 





A circle in a square in a circle in a square 
20110329 

From George: A circle within a square which is inside
a larger circle which is also within a square.
(a circle in a square inside a circle in a square)
Equation of the smaller circle is: x ^ 2 x y ^ 2 = 25.
What are the dimensions of the larger square?
Been 40 years, trying to help my son. 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. 





Points with distance 5 from the point (2, 1) 
20110119 

From Alexa: Find all points having a xcoordinate of 2 whose distance from the point (2, 1) is 5. Answered by Penny Nom. 





A man made circular lake 
20101125 

From ailish: A man made circular lake has a diameter of 338 m. A bridge is to be constructed across the lake in such a way that it is 119 m away from the center of the lake. How long is the bridge? Answered by Penny Nom. 





The equation of a circle 
20101020 

From Silvan: Hi, I just want to find the x,y values for the circumference of a circle...
Lets take a clock having its centre at (0,0) in a graph.
I just want to know how to find the (x,y) coordinates for the curved path or the surface of the circle..
Is there any formula to directly align the curved path or the circumference of the circle in a graph for a known radius of a circle..
I feel it will be useful for me to draw a clock in a graph... :) Answered by Penny Nom. 





A truck goes south and then east 
20100826 

From MARK: A truck starts at point A and drives South 3 miles. Then it turns left at Point B and drives east four miles to point C. How many miles is the truck at point C from point A if it were to drive directly from point A to Point C.My book says the answer is 5 miles. How did they come up with the answer? Answered by Robert Dawson. 





Two overlapping circles 
20100804 

From Husen: two circles of radius 5 cm intersect each other .the distance between their centers is 5root 2.find the area of the portion common to the two circles Answered by Penny Nom. 





The equation of a circle 
20100623 

From Michelle: Write and equation for the circle with a center, (0,0) and a diameter of 12 Answered by Penny Nom. 





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. 





A square inscribed in a circle 
20100525 

From Middle: what is the perimeter of a square inscribed in a circle of radius 5.0 inches? Answered by Penny Nom. 





How far is the runner from the starting point? 
20100522 

From Richard: A marathon runner runs 6 miles south and then 8 miles east. How far is the runner from the starting point? Answered by Tyler Wood. 





How far am I from the starting point? 
20100518 

From jilayna: if i walk 5 miles north, 7 miles east, and 3 miles north again.to the nearest tenth of a mile ,how far,in a straight line, am i from my starting point Answered by Penny Nom. 





A ladder against a wall 
20100325 

From amber: the distance from the bottom of the ladder to the building is18 foot less than the length of the ladder.How high up the building is the top of the ladder if that distance is 1 ft less than the length of the ladder? Answered by Penny Nom. 





The hypotenuse 
20100227 

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





A 25 foot ladder reaches a window 20 feet high 
20100227 

From Tanner: a 25 foot ladder reaches a window 20 feet high. how far is the ladder from the building? how far must the foot of the ladder be moved to lower the top of the ladder by four feet? Answered by Tyler Wood. 





The center of a rectangular room 
20100216 

From Diana: Consider a rectangular room, 15 feet wide, 30 feet long and 12 feet high. What is the exact distance from any of the 8 corners of the room and its geometric center? Can you write a generic formula for such a distance? And if we keep the same proportions on all dimensions, can you write an expression for the same distance as a function of the floor perimeter? Answered by Penny Nom. 





Loading a headboard in a uhaul 
20100120 

From gina: I have a uhaul 9'10" long 4"9"wide 4'7"height I have a headboard 74 inches in height would it fit the box diagonally Answered by Penny Nom. 





How high up the building does the ladder reach? 
20100119 

From rosenda: A 10 meter ladder is 6 meter from the base of a building. How high up the building does the ladder reach? Answered by Robert Dawson. 





Related Rates Problem 
20100112 

From Neven: A woman raises a bucket of cement to a platform 40 ft
above her head by means of a rope 80 ft long that passes
over a pulley on the platform. If she holds her end of
the rope firmly at head level and walks away at 5ft/s,
how fast is the bucket rising when she is 30 ft away
from the spot directly below the pulley?
(G. F. Simmons, Calculus with Analytic Geometry, pg.142) Answered by Penny Nom. 





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 ladder leaning against a wall 
20090908 

From Mackenzie: A 7 foot long ladder is leaning against the building. The foot of the ladder is 2 feet from the base of the building. How far up the wall is the top of the ladder? Answered by Stephen La Rocque. 





A walkway through a park 
20090307 

From felicia: a diagonal walkway through a park is 18 meters long. If the park is a square, how long is one of its sides to the nearest tenth of a meter? Answered by Penny Nom. 





An octagonal landscaping frame 
20090301 

From Richard: Hi
I am trying to put landscape timbers down in octagon shape that measures 6
feet across and outside measures 360 degrees.. The timbers are 4 inches by 4
inches. I need to know at what angle to cut boards and at what length i need to
complete octagon.
Thanking you in advance for your kind assistance.
Richard :) Answered by Harley Weston. 





The floor area in a spherical space station 
20090214 

From Ed: I am writing a science fiction novel that involves a spherical space station with a
radius of 800 meters. Inside, artificial gravity allows parallel floors set 4 meters
apart. If you count the floor that has a radius of 800 meters as Floor 0, then the
next floor up (Floor +1) would by 4 meters above the surface of Floor 0. There
would then be Floor 1 4 meters down from Floor 0. This would continue until
you reach the top or bottom floor, where there is at least 4 meters but less than
8 meters to the top or bottom of the sphere. Obviously the top and bottom
floors would have the (same) smallest area, while Floor 0 would have about 2
million square feet.
My problem is figuring out the total area of all of the floors, or for that
matter, any particular floors or the total number of floors (the total of all the
+ floors, the  floors (these numbers will be the same) plus Floor 0.
Ed Answered by Penny Nom. 





How far is the airplane from the control tower? 
20090117 

From Murtaza: An aircraft is vertically above a point which is 10 km west and 15 km north of a control tower. The aircraft is 4000 m above the ground, how far is it from the control tower? Answered by Penny Nom. 





Insulation in an attic 
20081118 

From Scott: A homeowner wishes to insulate her attic with fiberglass insulation to
conserve energy. The insulation comes in 40cmwide rolls that are cut
to fit between the rafters in the attic. If the roof is 6 m from peak to eave
and the attic space is 2 m high at the peak, how long does each of the
pieces of insulation need to be? Round to the nearest tenth. Answered by Harley Weston. 





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. 





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. 





A square with diagonal 200 metres 
20080820 

From kelvin: find the are and perimeter of a square with diagonal of 200 meters? Answered by Penny Nom. 





The length of a side of a square 
20080727 

From FRANK: WHAT IS THE LENGTH OF ONE SIDE OF A SQUARE WITH A DIAGONAL OF LENGTH 2 TO THE HALF POWER Answered by Stephen La Rocque. 





How far away is the horizon? 
20080613 

From Ali: A plane is 10km above the earths surface, and you want to know how far away the horizon is, you know that the radius of the earth is about 6400km, how far away is the horizon along the earth's curved surface. My teacher has drawn a diagram; a circle representing the earth with one vertex at the center of the earth, another vertex outside the cirlce representing the plane (the distance between the earth and plane is 10km) and the last one is on the circle representing the horizon. Could you please explain how I would solve this problem, thanks! 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. 





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. 





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. 





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. 





How far is she from her starting point? 
20080330 

From Nancy: A child runs due east for 23.5m and then she runs 10.5m due south. How far is she from her starting point? 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 diagonal of a rectangle 
20080221 

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





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. 





A wiffleball field 
20071031 

From Svitlana: The Adam's family has set up a wiffleball field in their backyard. The bases are arranged like a typical baseball diamond, where the distance between consecutive bases is the same. First base is opposite of third base, and second base is opposite of home plate. The distance between consecutive bases is 50 feet. Now, the pitcher stands 25 feet from home plate and lies on the line between home plate and second base. How far is the pitcher from first base? Round your answer down to the nearest inch. Answered by Penny Nom. 





How to solve related rates problems 
20071027 

From David: Can you plz explain how and where you come up with an equation to solve this?
Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second. Answered by Stephen La Rocque. 





Finding radius given chord length and distance to center 
20071004 

From Venus: a chord of 48mm long is 7mm from the center of the circle. What is the radius of the circle? Answered by Stephen La Rocque. 





Building a garage 
20070729 

From charles: I want to build a garage that is 24 feet 4 inches wide by 50 feet long.
can you please tell me what the length of one corner is to the other? Answered by Penny Nom. 





Some trig problems 
20070720 

From Jocelyn: I wasn't able to solve this equation:
only find the function using Pythagorean theorem
Please help me....
sinA = 3/4 find secB
tanA = 3/4 find cosA
sinB = 4/5 find tan A
cosA = 5 find csc A
b =5; a= 12 find sin A
c =25; a = 24 find cot A
a = 6; c =10 find b?
Find B when c = 25; a = 24
Find A when a = 5 and b = 12
csc = 1/2 find cos Answered by Penny Nom. 





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. 





A circle inside a square 
20070531 

From Mer: there is a circle inside a square... there is a shaded rectangle that measures 5mm X 10mm and they want to know what the radius is. The edge of the shaded rectangle touches a point on the circle. Answered by Penny Nom. 





A point on a semicircle 
20070528 

From arun: a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle? Answered by Penny Nom. 





How far apart are the cars? 
20070407 

From ian: 2 cars set off in opposite directions and travel for 6 miles,
they both take a left turn, and travel for a further 8 miles...........
how far apart are the cars???
a) 10 miles
b) 22 miles
c) 20 miles
d) 18 miles Answered by Penny Nom. 





a^2 + b^2 = c^2 
20070304 

From Colburn: 27 feet long base 14 feet height what is the diagonal Answered by Stephen La Rocque. 





Line segments on dot paper 
20070121 

From Khaori: The three line segments below are drawn on centimeter dot paper.
a. Find the length of each segment to the nearest tenthousandth of a centimeter. b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not. Answered by Penny Nom. 





A rhombus 
20061226 

From Jose: show mathematically that a quadrilateral whose vertices are A(2,1),B(6,2) C(10,1),and D(6,4) is a rhombus 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. 





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. 





Constructing a fence 
20050809 

From Andres: I was constructing my fence and was having some problems trying to do a perfect (or as close as possible) arch. If i know a section of a fence is for example 85 inches wide and I want a 4 inch rise from the top rail how do i figure out the radius? Answered by Penny Nom. 





Practical applications: parabolas and Pythagoras 
20041024 

From Connie: Provide two examples of real life objects that incorporate parabolic shapes. Explain the reason why the parabolic shape was used in each object.
I need at least one practical application of the Pythagorean Theorem. Answered by Penny Nom. 





Pythagoras in everyday life 
20041013 

From Tiffany: I was wondering if you have any reallife uses of the pythagorean theorem that you use in your everyday life. Answered by Penny Nom. 





The area of a lot 
20040929 

From Deb: I am trying to figure out how many square feet are in a piece of property. Start at Point Athen go 140 feet norththen 100 feet due eastthen 300 feet at an angle southeast so that connecting to point A would be a straight line (right angle to first line north.) Answered by Penny Nom. 





The length of a cut 
20040917 

From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures:
a=4squared, b=6squared.
She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif. 





A cube is inscribed inside a sphere 
20040818 

From A student: A cube is inscribed inside a sphere with radius sqrt8cm. Find the
(a) length of the cube
(b) volume of the space inside the sphere but outside the cube. Answered by Penny Nom. 





An Octagonal playhouse 
20040713 

From Levi: I'm building an octagon playhouse for my son that is 8 feet wide.
what would be the measurements of each of the eight sides. Answered by Harley Weston. 





How far apart are they? 
20040523 

From A student: 2 cars start at same loc. drive opposite direction for 6 miles then they each turn left and travel for 8 miles how far apart are they? Answered by Penny Nom. 





Bundles of asphalt shingles 
20040124 

From Larry: According to my study material 4:12 multiplying factor for shingles is 1.054. The question reads as follows: A building with a floor plan of 3350 sq. ft. and a roof slope of 4:12 will require _______ bundles of standard asphalt shingles. Answered by Harley Weston. 





The volume of a cube 
20031122 

From A student: i have a cube, and the line that cuts threough the middle of the cube across to the other side is 4 radical6. what is the volume of the cube? 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. 





The general equation for a sphere 
20030911 

From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom. 





Two cars 
20030709 

From Nicole: Two cars start off at the same point on a striaght highway facing opposite directions. Each car drives 6 miles, talkes a left turn, and drives for 8 miles. How far apart are the two cars. 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. 





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. 





Pythagoras in three dimensions 
20021014 

From Miki: A room is 6m long, 5m wide and 3 m high. Find the distance from the corner of the floor to the opposite corner of the celing. Answered by Peny 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. 





An octagonshaped deck 
20020220 

From An instructor: How can you solve for finding the side measurements of an octagonshaped deck that is 10 feet long and 10 feet wide. 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. 





Two geometry problems 
20000909 

From Becky: What are all the real values of x that are solutions for the inequality [x2] < 6? ( it's less than or equal to) What is the distance between the points with (x,y) coordinates (3,2) and (3,1)? Answered by Peny Nom. 





Triangles, The Pythagorean Theorem and Pizzas. 
19970223 

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. 

