







A cylinder with a cone on top 
20190116 

From Berania: A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a height of 15 feet. The roof has an inclination angle of 25 degrees.
(a) Determine the height of the cone to the nearest tenth of a foot.
(b) Determine the overall volume of the tower to the nearest cubic foot. Answered by Penny Nom. 





The height of a tower 
20181212 

From Pandey: Hello sir plz solve this question. If the shadow of a tower is found to be 10.5m longer when the sun's altitude is 45°AND60°. Find the height of the tower. Answered by Penny Nom. 





Find the height of the tower 
20130428 

From nombulelo: the shadow of a tower,when the angle of elevation of the sun is 30 degrees is found to be 40 meters longer than when it is 45 degrees. Find the height of the tower Answered by Penny Nom. 





The height of a tower 
20120106 

From trevor: A tower is on the top of a hill. It is 2,400 feet from an observer to a point directly under the tower and at the same elevation as the observer. The angle of elevation from the observer to the base of the tower is 15 degrees and to the top of the tower 23 degrees. How tall is the tower in feet? Compute your answer within one foot. Answered by Penny Nom. 





Line of sight 
20100506 

From David: I live in St. Joseph, Michigan and there is an ongoing argument regarding lineofsight over the horizon.
Standing on a 200 foot high bluff here, people swear they can see the top of the Willis (nee Sears) Tower in Chicago, which is about 1653 feet high.
It is my contention that this is actually a "refracted reflection" and not directlineofsight.
So, to settle the argument, I'd sure like some simple explanation for this, even ifand I hope notI am incorrect.
David Answered by Harley Weston. 





A champagne tower 
20100416 

From gabriel: thanks for having something like this up online. My question is how do i build a Champagne Tower that has 290 glasses and 15 stories high.
Please help me out. this is for a clarity function. Answered by Robert Dawson. 





A radio tower 
20100326 

From Alex: The height of a radio tower is 450 feet, and the ground on one side of the tower slopes upward at an angle of 10 degrees. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 110 feet from the base of the tower? Answered by Harley Weston. 





The leaning tower of Pisa 
20090809 

From MF: Would you have any idea how the 'latitude of 44 degrees N" has anything to do with this question and how I would apply it?
The leaning tower of Pisa leans toward the south at an angle of 5.5 degrees. One day near noon its shadow was measured to be 84.02 m long and the angle of elevation from the tip of the shadow to the top of the tower was measured as 32.0 degrees. To answer the question, assume that the tower is like a pole stuck in the ground, it has negligible width. Also, it is important to know that Pisa Italy is at a latitude of approx 44 degrees North because this affects the direction of the shadow.) Answered by Stephen La Rocque. 





A vertical radio tower is located on the top of a hill 
20090421 

From Rafael: A vertical radio tower is located on the top of a hill that has an angle of elevation of 10 degrees. A 70foot guy wire is attached to the tower 45 feet above the hill.
a. Make a drawing to illustrate the situation
b. What angle does the guy wire make with the side of the hill?
c. How far from the base of the tower is the guy wire anchored to the hill?
What confuses me about this problem is the visual situation. Isn't the angle of the guy wire with the side of the hill the same as the angle of elevation? And if not, then how is one supposed to find the other angles without any more information? Answered by Harley Weston. 





How tall is the tower? 
20080313 

From chris: you are standing 120 feet from the base of a tower. the angle of the elevation to the top of the tower is 15 degrees. how tall is the actual tower? Answered by Penny Nom. 





The swaying of a building in the wind 
20070811 

From San: During a strong wind, a tall builing, such as the CN Tower, can sway
back and forth as much as 100cm, with a period of 10 seconds.
Please help me to determine the equation for this function, in the form
y=asinkx Answered by Stephen La Rocque. 





Height of a tower from two observations 
20070716 

From joyce: An observer wishes to determine the height of a tower. He takes sight @
the top of the tower from A & B w/c are 5oft. apart @
the elevation on a direct line w/ the tower.
The vertical angle @ point A is 30 degrees & the point B is 40 degrees.
What is the height of the tower?
Find the value of x in angle tangent 40 degrees and 30 degrees?
Show the solution of the value of x? Answered by Stephen La Rocque. 





Finding the legth of a guy wire 
20061015 

From Aubrey: a radio tower 500 feet high is located on the side of a hill with an inclination to the horizontal of 5 degrees. how long should two guy wires be if they are to connect to the top of the tower and be secured at two points 100 feet directly above and directly below the base of the tower? Answered by Stephen La Rocque. 





The volume of water in a sphere shaped water tower 
20060514 

From Dan: I work in the water industry, providing automatic controls for water systems. I was wondering if there was a formula for calculating the volume of water in a sphere shaped water tower? With the use of a pressure gauge we know the elevation of zero water {the bottom of sphere) and the overflow elev. (near the top of sphere) I would like to calculate how many gallons are at any elevation in between. Answered by Stephen La Rocque. 





The height of a tower 
20051108 

From Vinita: Observers at point A and B, who Stand on level ground on opposite sides of a tower, measure the angle of elevation to the top of the tower to be 33 degrees and 49 degrees respectively. Another point C is 120 m from point B, Triangle ABC =67 degrees and BAC = 31 degrees. Find the height of the tower to the nearest metre. Answered by Penny Nom. 





If the distance of a person from a tower is 100 m... 
20050215 

From Agustin: If the distance of a person from a tower is 100 m and the angle subtended by the top of the tower with the ground is 30 degrees, what is the height of the tower in meters?
Answered by Harley Weston. 





towers of cubes 
19991005 

From Sanker: I need help to solve this Rules for bulding towers of cubes rule 1  The number of cubes on the bottom layer is always one less than the number of squares on the grid  rule 2  Each new layer is made with one cube less than the layer underneath it.   Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid
 investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid
 investigate the relation between the number of arrangements of cubes and the size of the grid
 when there are two layers of cubes
 when there are more than two layers of cubes
Answered by Walter Whiteley. 





Towers of Hanoi 
19990903 

From Jeni: In the puzzle called the Towers of Hanoi there are three peg and you are asked to move the rings from one peg and stack them in order on another peg. You can make as many moves as you want, but each move must consist of moving exactly one ring. Moreover, no ring may be placed on top of a smaller ring. The minimum number of moves required to move n rings is 1 for 1, 3 for 2 rings, 7 for 3 rings, 15 for 4 rings, and 31 for 5 rings. Find a formula for this sequence. What is the minimum number of moves required to move 6 rings? Answered by Penny Nom. 

