







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. 





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. 





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 barn roof 
20160529 

From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. 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. 





A deck that is half an ellipse 
20160228 

From Steve: On your website, I was reading a question and your response from a girl named Angela in which you provided a formula by which her father, a welder, could figure out points on an arc corresponding to equal 3' intervals on a 30' chord where the vertex was 1' off the chord. Is there an equivalent formula when working with an ellipse? I suspect this change will make the calculations significantly more complex. I am building a deck that is half an oval, and would like to be able to mark out the perimeter by measuring the distance from regular intervals on the primary access to a corresponding point on the perimeter. I will then connect the points on the perimeter and cut a reasonably smooth arc. The length of the primary access will be 22' and width of the deck at the vertex is 9'. I would like to be able to know the distance from the primary axis to a point on the perimeter at equal intervals of 6" along the primary axis. Can you help? Answered by Penny Nom. 





The distance between two boats 
20150726 

From mohammad: Two boats leave the same dock at the same time,one traveling due east at 10 mph and the other due north at 24mph,how many miles apart are the boats after 3hours ? 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. 





Covering a 12 inch by 12 inch square hole 
20140702 

From Patricia: I am putting in a new bathroom fan. I am wondering if a new light with a 15 inch diameter will cover the existing square hole which is 12 by 12 inches? If the existing hole is 11 1/2 by 11 1/2 inches?
Also, if the 15 inch diameter does not cover the 12 by 12 hole, what size diameter would?
Thank you. Answered by Penny Nom. 





The Pythagorean Theorem 
20140330 

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





The fourth side of a quadrilateral 
20140123 

From joanna: left vertical measurement 2560mm
right vertical measurement 1850mm
base horizontal measurement 1750mm
question  what will the 4th measurement be please.
using a scale drawing I make it approx 1900mm but require an accurate measurement
regards
Joanna Answered by Penny Nom. 





A rectangle inscribed in a circle 
20140110 

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





A scalene triangle 
20140107 

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





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. 





A square inscribed in a circle 
20131014 

From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom. 





The equation of a circle 
20130211 

From mhd: Complete the equation of the circle centered at(0,4) with radius 3 Answered by Penny Nom. 





Milling round stock to square stock 
20121217 

From Bryan: Question from Bryan:
I want to know what the smallest diameter round is that will make a 31/4" square? Is there a formula for that? I am milling round stock into square.
Thank you. Answered by Harley Weston. 





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 storage box with a slanted roof 
20120213 

From Sophia: Hi!
I have another problem.
The diagram shows a side view of a box which is used to store small logs of
wood for burning in a fire place. The slopping lid has an overhand of 15cm.
a) Calculate the total length of the slopping lid to the nearest cm.
b) When the lid is open above ground will the end of the lid be?
P.S. Please see attached. 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. 





A cube inscribed in a sphere 
20120123 

From Gelo: What are the largest volume and total surface area of a cube that may be inscribed inside a sphere whose radius is 5 kilometers. Answered by Walter Whiteley. 





A straight line distance 
20120106 

From Margaret: If you traveled 300 miles east and 275 miles north, how many miles would you save by going in a straight line? Answered by Penny Nom. 





The area of a triangular garden 
20111031 

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





A pyramid and Pythagoras 
20111015 

From ele: On square based pyramid, the lengths of the sides of the base are all 2m. The height from the top of the pyramid to the middle of the base is 0.5m. What are the lengths of the sides of the triangular pieces and the contained angle? 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. 





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. 





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. 





Two chords in a circle 
20101202 

From girma: one chord of a circle is 8cm long and it's distance from the center is 4cm long.what will be the length of another chord, of the same circle ,which is 2cm from the center 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. 





Constructing a tipi 
20100920 

From mike: we are thinking about making a lightweight tipi tent but we need to know what the angles and lengths of each side that we will need to cut. The height of the tipi wants to be about 2.2m span at the widest point wants to be about 3.2m we want to make it based upon a 6 sided(hexagon) shape thanks for your help Answered by Harley Weston. 





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. 





A play tent 
20100628 

From Susan: Hi!!!
I am making a play tent as seen at the link below and need to figure out how to get the dimensions for the cone shape. The one shown has 4 different seams, but I guess I can get away with just one seam to sew it together (?) I need it to go over a hula hoop as that is what I am using for the round support at the top. My hula hoop is
35" in diameter from outside edge to outside edge. I would like the height of the teepee to be around 30" from the center to the peak.
Thanks so much, oh my gosh, I have been fretting for 2 days about this and my hair is about to fall out!!!!
Please contact me if you need any additional info.
~Susan
http://www.landofnod.com/family.aspx?c=52&f=4100 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. 





The low leg height of a shutter 
20100520 

From brian: I work for a shutter company and am in need of a formula to figure
out what the low leg height would be if given the width of shutter,
the high point of arch top and the radius. example would be a 18" wide
shutter with a 80" high leg on the right side and a 30" radius. I would
need a way to figure what the low leg height (left side of shutter)
would be. Or if given width, low leg height and radius what the high
side would be? If any of this can be given in laymen's terms it would be
much appreciated.
Thanks,
Brian Answered by Harley Weston. 





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. 





A square corner 
20100211 

From Trevor: I am building a new house and wish to set it out on site with the use of
profile boards and string. I want to be certain it is correct in terms of
squareness. I have a vague idea that the square on the hypotenuse should
be equal to the sum of the squares of the other two sides.
I get a little lost here and need some help. The building is a rectangle
measuring 40x30 feet to exterior brickwork. I guess that the length
of the hypotenuse should be exactly the square root of the combined
squares of the two sides.
Using the above measurements could you give me calculations from nuts
to soup as to the correct length of the diagonal. And what adjustments
are needed if everthing is not in accord.
Trevor. Answered by Robert Dawson. 





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 quilt square 
20100107 

From Kimi: A quilt square is stitched along each diagonal to make 4 right triangles.
Each diagonal is 12 inches long. ( 1 foot)
How many quilt squares can be cut from a piece of fabric that is 8 feet
long and 2 feet wide?? Answered by Penny Nom. 





A baseball diamond 
20091118 

From maelee: the official distance between home plate and second base in baseball diamond is 120ft. Find the area of the official ball diamond & the distance between the bases. Answered by Robert Dawson, Chris Fisher and Penny Nom. 





A computer screen 
20091118 

From Leonard: Whats the pythagorean theorem of computer measured 12"x 12" in length and width, whats the diagonal measurement in 15". Thank You Answered by Penny Nom. 





A problem in a hexagon 
20091107 

From WIlliam: I have a regular hexagon and all sides are 8 cm. I need to find the line segment
point a to point b. Point B is on the top left of the hexagon and the Point A is on the
middle right side, I know the line pass through 2 Equilateral triangles, I'm just not
sure how to do the equation.
Also how would you measure a line that goes right in the middle from one end to
the other Answered by Harley Weston. 





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. 





Segments of a ring gasket 
20090920 

From Robert: I am in the process of making an Excel spreadsheet in which our sales
team just needs to enter the outside diameter, inside diameter, and
number of segments to price ring gaskets that are too big to fit on a
sheet of material and need to be cut into segments. With your help I
was able to create a spread sheet that can calculate the Chord lengths,
and Segment height on a single gasket segment. I am now stuck trying to
come up with a formula to figure out the height of the second segment
when it is stacked on the first segment, then use it to add more
depending on the quantity of segments needed. I have an illustration
below showing 2 segments (of a gasket that was segmented into 4 pieces)
stacked together. I need to find a formula to get the dimension from
"A" to "B". Answered by Harley Weston. 





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 paper towel roll 
20090819 

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





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. 





The hypotenuse of a right angled triangle 
20090511 

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





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. 





The length of a ladder 
20090330 

From Susan: The foot of an extension ladder is 7 ft. from a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive integers. How long is the ladder? Answered by Penny Nom. 





Uses of Pythagorean theory 
20090327 

From Britta: Please, give me some complex real life situation examples where the pythagorean theory is used. It must be a grade 8 or grade 9 level of thinking as that is what is my teacher's demands. Answered by Robert Dawson. 





Octagonal panels for a horse pen 
20090325 

From Tony: I am building a pen for my horse. I am going to use 12' panels in the shape of an octagon. How many feet will he have from side to side using 12' panels.
Thanks,
Tony Answered by Robert Dawson and Penny Nom. 





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. 





A silo with a flat side 
20080714 

From Amy: Without using the Pythagorean Theorem, determine the capacity of a silo in cubic feet of grain if: the cylindershaped silo has one flat, rectangular face that rests against the side of the barn; the height of the silo is 30 feet and the face resting against the barn is 10 feet wide; the barn is approximately 5 feet from the center of the silo. Answered by Harley Weston. 





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. 





A problem with a kite 
20080528 

From randee: A kite that has been secured to a stake in the ground with a 20 foot string. The kite is located 12 feet from the ground, directly over point x. what is the distance, in feet between the stake and point x 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. 





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. 





10 squares drawn one inside another 
20080225 

From Rajesh: There are 10 squares drawn one inside another.The diagonal of the inneremost square is 20 units. if the distance b/w the corresponding corners of any two successive squares is 1 unit, find the diffrence between the areas of the eigth and seventh square counting from the innermost Answered by Stephen La Rocque. 





The diagonal of a rectangle 
20080221 

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





How tall is the pole? 
20080206 

From GENEVAMILTON: A WIRE THAT IS 6 FEET LONG IS ATTACHED TO A THE TOP OF A POLE THE WIRE IS ANCHORED IN THE GROUND AT 4 FEET FROM THE BASE OF THE POLE HOW TALL IS THE POLE? Answered by Stephen La Rocque. 





Out of school applications of Pythagoras Theorem 
20080123 

From Laura: Hi,
I am currently working on a math summative in which I have to choose a real life subject and relate it back to the material in my grade 12 math class. I find the history and discovery behind the Pythagorean Theorem and Identity very interesting, but I have yet to find a reallife application of the equations. Yes, I know they are used for finding distances, heights etc., but realistically, how many people actually use it in those situations? Very few. I was hoping for a new application. Is the pythagorean theorem (sin^2x + cos^2x = 1) even applicable? Thank you,
Laura Answered by Harley Weston. 





The distance back to school 
20080116 

From priya: a boy starts travelling from his house to his school. He travels 1 km east and then
2km north and then 1 km East and 1km North and then 1 km east and then 1 km North.
find out the shortest distance for him to reach his shool? Answered by Harley Weston. 





A plywood sheet in a doorway 
20080110 

From albetel: adoor is 7 feet tall and 36 inches wide. what is the widest sheet of plywood that can fit through the door? 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. 





Points that are 15 units from the origin 
20070920 

From Paula: Find the coordinates of any point(s) 15 units away from the origin with an
xcoordinate of 9.
I was given the answer: (9,12) and (9,12), but I do not understand how these numbers
were calculated. Thank you for your help! 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. 





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. 





Pythagoras theorem in daily life 
20070717 

From sana: i would like to what are the 5 practical uses of the Pythagoras theorem in
daily life??? its for a math project
thanx a lot
sana Answered by Penny Nom. 





The volume of a cube 
20070623 

From Leah: I am having trouble finding the equation for this problem.:
What is the volume of a cube with diagonals of length 6 sqrt(3) cm?
answer: (BLANK) cm3 Answered by Penny Nom. 





Using the Pythagorean Theorem 
20070618 

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





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. 





Two concentric circles 
20070419 

From James: Two concentric circles have a chord running through the outer one. The chord is the tangent of the inner circle and is 14 cm.The outer circle is shaded and the inner circle is not. Find the exact area of the shaded region without using a calculator. Answered by Stephen La Rocque. 





Pythagoras was right 
20070411 

From Vineet: in a right angle triangle, hypotenuse side is less than the sum of other two
sides, how the square of hypotenuse is equal to the sum of squares of other two sides? Answered by Stephen La Rocque. 





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 right triangle 
20070405 

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





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. 





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 Pythagorean theorem 
20061212 

From Beth: In a pythagorean theorem can the sides of a right triangle be three consecutive odd integers Answered by Stephen La Rocque. 





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. 





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 area of a triangle 
20060901 

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





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

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





Designing a garage 
20060608 

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





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. 





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. 





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. 





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

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





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. 





Area of an octagon 
20051004 

From AJ: I am working a project for my shop class and need to know the square footage for an octagon with equal 10foot sides. Answered by Penny Nom. 





The length of the side of an octagon 
20050922 

From Billy: How can you find the length of the side of an octagon when all that you know are the long sides of one of the eight perfect isc. triangles inside the octagon that share the same center point? 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. 





A pyramid 
20050424 

From Marc: I'm helping my daughter build a pyramid,it needs to be 30cm in height. I have cut out four pieces at 30 deg angles. When I went to join up the pieces it did not fit. I recheck my measuments and found that they were correct. Do I need to cut two pieces smaller so they can match up? Did I cut them at the wrong angles. My base is also 30cm, is that my problem? Answered by Chris Fisher and Harley Weston. 





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. 





The square root of 2 
20050312 

From Madhumita: From Pythagoras theorem we can draw square root 2 as a finite distance but it is irrational number which is endless. Explain how we can equate these two. Answered by Harley Weston. 





A diagonal in a cube 
20050306 

From Brett: A cube has a volume of 64 cubic inches. What is the length of segment AB? Segment AB is a straight line from the top left corner of the cube to the lower right bottom corner 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. 





Two Problems 
20040712 

From Justina: i cant figure out the range of this equation in interval form because the highest point seems to be a decimal. please help f(x) = x + sqrt(4x2)
.............................................................................
Building Design A circular air duct of diameter D is fit firmly into the rightangle corner where a basement wall meets the floor (see figure). Find the diameter of the largest water pipe that can be run in the rightangle corner behind the air duct. Answered by Claude Tardif and Penny Nom. 





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. 





A stained glass window 
20040329 

From Kay: I'm doing a stain glass project and it's on a 4 foot across octagonal window...and I'm trying to set up the pattern and I don't know how long the sides are! Answered by Penny Nom. 





A water lily 
20040317 

From Inba: A water lily with a rigid stem extends one foot above the surface of the water. When pulled over, it disappears beneath the water at a distance 3 feet from where the stem originally entered the water. How deep is the pond? 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. 





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. 





A 16 foot ladder 
20030904 

From Kelly: Two buildings are separated by a threefoot alleyway. Fatima wants to use a 16 foot ladder to reach a window in the wall of one of these buildings. If she places the foot of the ladder against the base of the other building, how far up the wall will the top of the ladder reach?? 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. 





A tangent to a circle 
20030418 

From Lech: The line with equation y=mx is a tangent to the circle with equation x2+y26x6y+17=0. Find the possible values of m. Answered by Harley Weston. 





The height of an equilateral triangle 
20030406 

From Rosa: If Each side of an equilateral triangle is 10 m. What is the height? Answered by Penny Nom. 





A triangle and a circle 
20030321 

From Jynks: We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle. Answered by Penny Nom. 





An arc of a circle 
20030312 

From Melissa: A strip of wood is 16 ft. long and is bent in the arc of a circle. Two radii, from the center of the circle to the ends of the arc, form a right angle. What is the approximate distance from one end of the wooden arc to the other? 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. 





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. 





Euclid and Pythagoras 
20010614 

From Scott: Question 1. In about 300 BC Euclid recorded a proof of Pythagoras rule. Disscuss Euclid's contribution to developing the theroem. Question 2. Why was it named after Pyhagoras if he did not orginally discover it? Answered by Chris Fisher. 





The diagonal 
20010328 

From Candace: Building measuring 40 feet 3 inches by 50 feet 3inches What is the measurement of the diagonal of the building? What was method of obtainin answer? Answered by Andrei Volodin. 





Mr. Moser's roof 
20010221 

From Michelle: Mr. Moser is planning to replace the roof of his home. He needs to order a pack of shingles. Each pack covers 100 sq. ft. of roof. Without a ladder, Mr. Moser can not climb to the roof to measure it. Instead, he measures his attic and finds it to be 40 ft. long, 24 ft. wide, and 5 ft. high at the peak of the roof which is in the center of the house. Although the roof is even with the side walls, he estimates the roof line continues 1.5 ft. beyond the front and back walls. How many full packs of shingles should Mr. Moser order to cover his roof? 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. 





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 aspect ratio of a rectangle 
20001204 

From Ron Delavigne: The aspect ratio of this rectangle is 4:3. That is A to B is 3. And B to C is 4. If I know the lenght of A to C is 19 inches, how can I find the length of A to B, and B to C. Answered by Penny Nom. 





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. 





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. 





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Two contest problems 
19990414 

From Bruce Baldwin: We have students that are preparing for the Pythagoras Contest which is a nation wide Grade 6 math challenge. In the preparatory tests we have run into several questions that we can not understand. Is there anyone who can help us?  If 1 * 9 = 0, 9 * 8 = 72, 2 * 8 = 9, then 9 * 9 = ?
 ...
Answered by Judi McDonald and Walter Whiteley. 





Pythagorean theorem research project 
19981231 

From Mohammed Hasan: Hi my name is Mohammed Hasan. I am a math honors student in 8th grade. I have to do a research project in math. The only problem is that I have to do the research project at a 10th grade level. I am having trouble raising the project at a tenth grade level. Would you please kindly take your time to give me some tips and web sites that will help me raise the Pythagorean theorem to a 10th grade level. Answered by Jack LeSage and Walter Whiteley. 





Curvature of the Earth 
19980316 

From Robert Dyck: How can I find the curvature per mile of the earths surface? What is it? Answered by Harley Weston. 





Pythagorean Triples. 
19971204 

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





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





Euclid's Pythagorean proof 
19960214 

From Sean: What is Euclid's proof of Pythagoras' theorem? Answered by Harley Weston. 

