Question

A conveyor belt leads from the ground to a bar door24 feet high. The angle between the belt and the ground is 32 degree. What is the length of the conveyor nearest foot?

Answer 1

45 feet

Explanation:

This is a classic right triangle trig problem. We have a reference angle, which is the angle made between the ground and the belt, of 32 degrees. The height up the side of the barn, which is the side across from the reference angle, is 24 feet. Which of our trig ratios relates side opposite to the hypotenuse? It's the sin ratio, so let's set it up and solve for the length of the belt, which is the hypotenuse of the right triangle.

`sin(32)=(24)/(x)`

Doing some algebraic acrobatics that with we get

`x=(24)/(sin(32))`

Plug that into your calculator in degree mode and you'll get 45.28991. Rounded to the nearest foot is 45 feet.