







A trough with a triangular cross section 
20160521 

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





The angles of a triangle 
20151217 

Faith pose la question : Does the measure of angle determine the length of its side? For example two angles are congruent then the sides are also congruent because from my understanding the angle determine the shape of triangle. Penny Nom lui répond. 





The length of a shadow 
20150801 

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





A barge of triangular cross section 
20140818 

tushar pose la question : a barge of triangular cross section is 20m long 12 m wide and 6m deep.its floats in SW at a draft if 4m find its displacement Penny Nom lui répond. 





The length of a shadow 
20140509 

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





Two cones 
20140409 

c.j pose la question : what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Penny Nom lui répond. 





Shadows of a father and son 
20140402 

esada pose la question : the father and son cast a shadow of 11 feet and 8 feet,respectively if the son is 4'8'' in height,how tall is the father? Penny Nom lui répond. 





A triangle construction 
20130727 

Nazrul pose la question : Two angles and the difference of the lengths of their opposite sides of a
triangle are given. How can I draw the triangle.
Please help me. Chris Fisher lui répond. 





Calibrating a conical tank 
20110205 

Bill pose la question : 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 Stephen La Rocque and Penny Nom lui répond. 





The height of a lamp 
20110113 

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





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

Rogerson pose la question : The point F is on the line through D(4, 0) and E(2, 6) so that DF=4DE. Find the coordinates of F. Penny Nom lui répond. 





A paper towel roll 
20090819 

Jeff pose la question : 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 Penny Nom lui répond. 





The position of the fulcrum 
20090523 

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





A 306090 triangle 
20090203 

Inez pose la question : If you have a 306090 triangle and the only side you get is 73 and a 90 degree box, how do you find the area? Penny Nom lui répond. 





The volume of a feed hopper 
20081218 

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





3 equidistant points 
20081201 

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





The midpoint o a line segment 
20081115 

Jane pose la question : The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Penny Nom lui répond. 





A flagpole and a yardstick 
20081107 

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





Similar Triangles Given a Median 
20080817 

RAM pose la question : Sides AB , AC and median AD of a triangle ABC are respectively proportional to
PQ PR and median PM of another triangle PQR. Show that ABC is similar to PQR Janice Cotcher lui répond. 





Similar triangles 
20080812 

ramarao pose la question : D is a point on side BC of a triangle ABC such that BD/CD=AB/AC. prove that AD is the bisector
AD is the bisector of BAC Chris Fisher lui répond. 





Similar triangles 
20080326 

Nisha pose la question : In triangle ABC, LM is parallel to AB. If AL=x3,AC=2x,BM=x2,BC=2x=3. Find x Penny Nom lui répond. 





A flagpole and a statue 
20080209 

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





Forces on an inclined plane 
20080110 

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





Lining up coins visually using geometry and trigonometry 
20071231 

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





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

Eva pose la question : A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Stephen La Rocque lui répond. 





Related Rates (streetlamp and shadow) 
20071109 

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





Surface area of an openended cone 
20071016 

Lorne pose la question : What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Stephen La Rocque lui répond. 





Similar triangles 
20070829 

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





Volume in a triangular water trough 
20070624 

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





Similar triangles 
20070221 

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





Height of a right triangle? 
20070129 

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





In the shadow of a building 
20070111 

Bill pose la question : if a building b feet cast a shadow f feet long, then, at the same time of the day, a tree t feet high will cast a shadow, how many feet long? Stephen La Rocque lui répond. 





How do the perimeters of the two pentagons compare? 
20070102 

Robert pose la question : If the area of one pentagon is eightyone times the area of another pentagon, how do the perimeters of the two pentagons compare? Penny Nom lui répond. 





The height of a building 
20061119 

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





How fast is the water level rising 
20060812 

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





Designing a garage 
20060608 

A builder pose la question : 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. Stephen La Rocque and Penny Nom lui répond. 





The volume of water in a cone 
20060321 

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





Heights and shadows 
20060306 

Debra pose la question : A person is 7 ft tall and his shadow is 10 ft tall. using the same info what is the shadow of a person who is 5ft tall
Stephen La Rocque lui répond. 





Water in a cone 
20040728 

A student pose la question : A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Penny Nom lui répond. 





A geometry problem 
20040304 

Jennifer pose la question : I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Chris Fisher lui répond. 





Two chords 
20031007 

Lori pose la question : Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Penny Nom lui répond. 





Water in a cone 
20030812 

Adrienne pose la question :
Water is poured into a tank in the shape of an inverted right circular cone.ð The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ð (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Penny Nom lui répond. 





Similar triangles 
20010908 

Dave pose la question : I am standing on the bank of a river ( whose banks are parallel here) directly opposite a boathouse, B, on the opposite bank. I walk along the bank of the river past a signpost, S, until I reach a point C distant 60 metres from where I started walking. I then walk away from the bank, at right angles to the bank, until I reach a shady tree at D. Attached to teh tree is a sign stating that this spot is 45 metres from the signpost. C is 36 metres beyond S and B and S are in line from D. (a) How far did I walk away from the bank of the river?? (b) Calculate the width of the river? Penny Nom lui répond. 





How tall is the tree? 
20010302 

Ronda pose la question : a tree's shadow is 42 ft. long. There is a stop sign that is right next to it and it is 18 ft. tall and it's shadow is 12 ft. long. How tall is the tree? Penny Nom lui répond. 





A lampost and its shadow 
20001224 

Laura pose la question : A lamppost line EC casts a shadow line AC. A 30 cm ruler line DB has been moved from A so that it's shadow falls just within the shadow of the lamppost.  Suppose the length of the ruler's shadow is 42 cm. What is the slope of the imaginary line AE?
 Suppose the lamppost's shadow is 15 m. long. How tall is the lamppost?
Penny Nom lui répond. 





Length of a shadow 
20001101 

Jessy pose la question : A man who is six feet tall is walking away from a street light that is fifteen feet tall. How long is the man's shadow when he is ten feet away from the light? Penny Nom lui répond. 





Two 12sided polygons 
19990925 

Kelly Boulton pose la question : Two 12sided polygons are similar. A side of the larger polygon is 3 times as long as the corresponding side of the smaller polygon. wHAT IS the ratio of the area of the larger polygon to the area of the smaller polygon. Walter Whiteley lui répond. 





A ladder problem 
19990422 

Michael Blade pose la question : 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? Penny Nom lui répond. 





Shimin's Geometry Problem 
19971202 

Ong Shimin pose la question : ABCD is a rectangle. X and Y are the midpoints of BC and CD respectively. W is a point on AB such that AW : WB = 2 : 1. Z is a point on AD such that AZ : ZD = 2 : 1. WY intersects XZ at O. If the area of triangle WOZ is 84 centimeters squared, find the area of triangle XOY. Chris Fisher lui répond. 

