Question

Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower end of the belt is 100 feet from the base of the silo and that the silo is 150 feet tall.

a. How long is the belt?
b. If we know the angle of elevation from the lower end of the belt to a window on the side of the silo is 45°, use special right triangle ratios to calculate the height of the window from the ground.
c. We need a ramp to the window. How long would it need to be?

Answer 1

We are given the dimensions of a silo that has a conveyor belt with a base length of 100 ft and the height of 150 ft.
a. The length of the conveyor can be obtained using the right triangle theorem using Pythagorean theorem where the sum of the squares of the legs is equal to the square of the hypotenuse. The length is the hypotenuse.
L^2 = 100^2 + 150^2 ; L = 180.28 ft.
b. Given the angle of elevation to the window is 45 degrees, the height of the window is obtained from tan 45 = height / 100 ft ; height of window = 100 ft.
c. The ramp of the window is the hypotenuse of the isosceles triangle whose legs is 100 ft. The length is equal to 141.42 ft.