







7 spheres on a hexagonal tray 
20190114 

From herm: what is the length of each side of a hexagonal tray, with the height of each side 0.75 inch, to hold seven spheres, each with a diameter of 3.00 inches? The spheres are placed such that each side of the hexagon is touched by one sphere at its midpoint (and the seventh sphere is place in the center of the "ring" of the other six spheres. Answered by Harley Weston. 





A rope fom a dock to a boat 
20180314 

From Tracey: A boat is tied with a rope to a dock that is 16 feet tall. Along, the water, the water the boat is 17 feet from the dock. How long is the rope connecting the boat to the dock? Let c represent the length of the rope.? Answered by Penny Nom. 





The Pythagorean Theorem 
20140330 

From brenae: The Pythagorean Theorem, what is it? Answered by Penny Nom. 





The development of the Pythagorean theorem 
20110408 

From Ataa: I am doing a assignment on Pythagorean Theorem and i am stuck on the subquestion
development of the Pythagorean theorem and i really need help can u give me accurate info
for this because i am not finding anything!!!thanks in advance.
Yours truly
AUMAKHAN Answered by Chris Fisher. 





Semicircles and the Pythagorean Theorem 
20110109 

From Jas: Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:
****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??
I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Answered by Penny Nom. 





The Pythagorean theorem 
20090624 

From supreet: What are some realworld applications of the Pythagorean theorem?
and
How are the Pythagorean theorem and the distance formula related? Answered by Harley Weston. 





Ladder Leaning on a Wall 
20090514 

From clinton: a ladder rests against a wall 24m high.the foot of the ladder is 7m from the foot of the wall. How do you calculate the length of the ladder Answered by Robert Dawson. 





The shadow of a tree 
20090420 

From Lindsey: James found that a 30 ft. tree that cast a shadow of 40 ft. A wire from the top of the tree to the beginning of its shadow must be how long? Answered by Penny Nom. 





Consecutive Even Integer Sides of a Triangle 
20080924 

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





The Pythagorean theorem with triangles rather than squares 
20080429 

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





Pythagorean equation 
20080227 

From Judy: X^2 + Y^2 = 5^2
Graph all ordered pairs in the coordiante plane that satisfy the Pythagorean equation, x squared plus y squared equals five squared 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. 





Diameter of an octagon 
20070807 

From Bree: I am trying to find the diameter of a octagon with 20' sides . What formula do I use? Answered by Stephen La Rocque. 





Find the area of a regular pentagon inscribed in a circle 
20070803 

From Tracy: Can you please help me with finding the area of a regular pentagon inscribed in a circle using the Pythagorean theorem. The radius of the circle is 5 cm and each side AB = BC = CD = DE = EA = 6 cm. Answered by Stephen La Rocque, Leeanne Boehm and Chris Fisher. 





Using the Pythagorean Theorem 
20070618 

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





Angles of depression 
20070613 

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





The area of a pyramid 
20070428 

From Alexander: Total area of the plate required to fabricate a vessel(pyramid) the base is 0.6mx0.6m and height of 1.0m. Answered by Stephen La Rocque. 





The Pythagorean theorem 
20070404 

From Cassandra: how do u find a and/or b using the Pythagorean theorem of a right triangle? Answered by Leeanne Boehm. 





Finding the vertical height of a roof 
20070305 

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





The hypotenuse 
20061002 

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





I need to cut an octagon 
20060923 

From Freddie: I have a 48 inch square piece of wood that I need to cut into an octagon, help. What's an easy way to just measure and cut it. Answered by Penny Nom. 





The length of 2 sides of a triangle 
20060915 

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





The Pythagorean relation 
20060509 

From Vicky:
How do you the Pythagorean relation to find the length of the hypotenuse x to one decimal place?
x^{2} = 3.6^{2}+ 5.3^{2}
My teacher, Mr. Mutrie, wants to know what this means?
SOH CAH TOA
Answered by Harley Weston. 





Cutting an octagon from a square 
20060507 

From Veronica: 1.A regular octagon is to be cut out of a square piece of metal which has sides of 1 metre. What will be the length of the sides of the octagon?
2.What will be the area of the octagon? Answered by Penny Nom. 





Pythagorus and cone dimensions 
20060426 

From Glynnis: How do you find the measure of a side that is not the hypotenuse using the Pythagorean Theorem? Also, how do you figure the surface area and volume of a cone when the radius is 5 yards and the height is 8 yards? Answered by Stephen La Rocque. 





The perimeter of a regular octagon 
20060420 

From Martin: I would like to make an octagon out of 2x4 lumber. I know that the lumber needs to be cut at 67.5 degree angles, but how do I determine the length of each piece if I want to make, say, a 2.5 ft diameter octagon? Answered by Stephen La Rocque. 





The area of a block of land 
20060326 

From Ronald:
I have a building block of land with four unequal sides and only one right angle. I want to know the total area (in metres) and how the calculations were carried out.
The four sides are: Rear of property: 9.14 metres
left side: 36.9 metres
Right side: 32.61 Metres
front to street: 27.43 Metres
The front to street and right side constitute a right angle. but there are no others. Answered by Penny Nom. 





A 25 foot ladder is leaning against a building. 
20060324 

From Ali: A 25 foot ladder is leaning against a building. The base of the ladder is 7 feet from the building. How high up the building does the ladder reach? Answered by Stephen La Rocque. 





The third side of a triangle 
20060209 

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





An irregular octagon 
20060120 

From Robert: I am building a poker table which is in the shape of an irregular octagon. I know the table measures 72 inches long and 48 inches wide with two parallel straight sides of equal length and six smaller sides of equal length ( three at each end of the table), what I don't know are the lengths of the any of the sides. Answered by Harley Weston. 





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

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





The area of an octagon 
20060103 

From Nikki: I want to figure out the square footage of an octagon. i have 8 panels that are 24" wide. Its for my dogs and i wanna know how much room they'll have. Answered by Penny Nom. 





Folding a sheet of paper 
20051215 

From Victoria: The current problem is to take a normal 8 1/2 x 11 sheet of paper, take a corner and fold it to meet the opposite corner, and (without actually measuring) produce a formula to describe the result fold/crease. Answered by Penny Nom. 





Triangles with integer sides 
20051104 

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





The sides of an octagon 
20051102 

From Royce: I understand there is a simple calculation to determine the sides of an octagon when you know the distance across the parallel flats. something like .447 . can you help? Answered by Penny Nom. 





A cube in a sphere 
20051019 

From Damian: A sphere passes through the eight corners of a cube side 10cm. Find the volume of the sphere. Answered by Penny Nom. 





A line that intersects a circle 
20051018 

From Bruce: I would like to solve the following problem illustrated below. How do you calculate the length of a line that intersects a circle. Answered by Penny Nom. 





City A is 30 miles directly north of City C 
20051004 

From A student: City A is 30 miles directly north of City C, and City B is 40 miles directly east of City C. Cities A and B are connected by a straight road. Find the length of the shortest path from City C to the road that connects A and B. Answered by Penny Nom. 





The area of a lot 
20050829 

From Richard: My wife and I are interested in buying property in Idaho but the owner can't give us a square footage of the lot. The dimensions are as follows:
121.0 on the left side
157.0 on the right side
135.0 on the bottom
162.0 on the top
The bottom right corner of the lot is a true right angle, the rest are not. 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. 





arccos(5/13) 
20050531 

From Kyle: I would like to know how to evaluate the problem of: Arccos 5/13. Answered by Penny Nom. 





The area of an octagon 
20050521 

From Jeremy: i need to find the area of an octagon with each side measuring 1 foot Answered by Penny Nom. 





A right triangle 
20050518 

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





Dimensions of a roof 
20050318 

From A roofer?: A right triangle (roof of a house) has a base of 7 feet and a 22 degree angle. What is the height of the roof and what is the hypothenus of the triangle. 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. 





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. 





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. 





Odd Pythagorean triples 
20031023 

From Kathleen: in a triple can a and b be odd numbers 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. 





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. 





Constructing the square root of 3 
20020607 

From Allan: I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge. Answered by Penny Nom. 





Bob swam across a river 
20020522 

From Torri: Bob swam across a river 420 ft wide. A strong current carried him 580ft downstream as he swam. Find x, the distance bob actually swam. Answered by Penny Nom. 





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. 





A clap of thunder 
20011115 

From Frustrated Mom: While getting a recipe for the Thanksgiving feast. The teacher was talking on the phone with a friend who lives four miles north of her. She saw a flash of lightning through the window: fifteen seconds later, she heard a clap of thunder. Ten seconds after that she heard the thunder over the phone. Where did the lightning strike in relation to the teacher's house. (There are two possible answers. Sound travels about 1/5 mile per second. Some people say it's not good to be on the phone in a thunderstorm). Answered by Claude Tardif and Penny Nom. 





Pythagoras & magic squares 
20011009 

From John: My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 345 triangle, and the fact that his teacher told him there was also a 51213 triangle, i.e. both rightangled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on. I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7order square would also generate a rightangled triangle for him. He found that 72425, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...  Is there a rightangled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and
 Is each triangle unique (or, as he put it, can you only have one wholenumbersided rightangled triangle for each triangle whose shortest side is an odd number)?
Answered by Chris Fisher. 





The hypotenuse of a right triangle 
20010122 

From Phillipe: How do you find the hypotenuse of a right triangle? Answered by Penny Nom. 





The Pythagorean Theorem 
20010108 

From Megan: Why the Pythagorean Theorem so important in our lives and what is it's history? Answered by Penny Nom. 





The pythagorean theorem in everyday life 
20010106 

From Josh: What are some ways that we use the pythagorean theorem in jobs, or even in everyday life? Answered by Claude tardif. 





The pythagorean theorem 
20000519 

From Lauren Fitzgerald: how do you find the length of th hipotnuse( or however you spell that word). i understand you have to add the two sides. but when i do add i always end up with this way off answer. i donot understand at all. Answered by Paul Betts. 





Pythagorean triples 
20000301 

From Bob Ross: Could you please tell me what pythagoria triad is.I am a year 10 student. Answered by Chris Fisher. 





The area of a garden 
19991217 

From Jessica Wells: Hi My name is Jessica Wells and I am 10 years old. I was hoping you could help me out wityh a question my dad gave me. It is if aq graden is 32cm in diameter and I want to know the area of it what process do I use? He's a math wiz so I need o show him that I'm smart too Answered by Penny Nom. 





Pythagorean Triples. 
19971204 

From Shameq Sayeed: I've got a couple of problems which I hope you'll be able to solve for me. I'm investigating pythagorean triples, and I have found a trend for the triples themselves, and thus have been able to form a general equation, i.e. a=2x+1, b=2x^2+2x, and c=b+1. Now, I sure this equation works, because I've tried it out and have come up with triples that adhere to a^2 + b^2 = c^2. But I was wondering WHY c=b+1. Is it possible to have c=b+2, and if not why not? THAT is the first problem. Answered by Chris Fisher. 





A Presidential Proof 
19970318 

From Greg Smith: Which US president developed a proof for the Pythagorean Theorem? Where can a copy of the proof be located? Answered by Chris Fisher and Harley Weston. 





The Real Pythagoras 
19970316 

From Michael Gaskin: I am wondering if you have any information about Pythagoras and his accounts in math. Answered by Chris Fisher. 





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. 





An application of Pythagoras' theorem 
19960409 

From Mike: We'd like to know what practical applications there may be for the Pythagorean theorem. Answered by Penny Nom and Maxine Stinka. 

