Question

Grain elevators are conveyor belts used throughout the Midwest to take grains, like wheat, to the top of a grain silo for storage.

If the belt makes a 60 degree angle with the ground and the belt is 42 yards long, how tall is the silo, in yards? Round your answer to the nearest whole number.

Answer 1

Explanation:

We can use trigonometry to solve this problem. Let's call the height of the silo "h". The opposite side of the triangle formed by the belt and the ground is "h", and the adjacent side is 42 yards. The tangent of 60 degrees is the ratio of the opposite side to the adjacent side, so we can write:

tan(60) = h/42

We can solve for "h" by multiplying both sides by 42:

42 tan(60) = h

Using a calculator, we find that tan(60) is approximately 1.732. Multiplying by 42, we get:

42 × 1.732 ≈ 72.8

Rounding to the nearest whole number, we get:

h ≈ 73

Therefore, the silo is approximately 73 yards tall.