Question

Grain elevators are conveyor belts used throughout the Midwest to take produce, like wheat, to the top of asilo for storage. The conveyor belt is approximately 70.7 feet long and rises from the ground at 45 degrees. What isthe height of the silo? Round to the nearest foot.

Answer 1

The conveyor belt is approximately 70.7 feet long and rises from the ground at 45 degrees. What is

the height of the silo?

Step 1

here we have a right triangle, we can use sine function

$\begin{gathered} \text{for a rigth triangle} \\ \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \text{isolate opposite side} \\ \text{opposite side=hypotenuse }\cdot\sin \theta \end{gathered}$

then,

Let

conveyor belt = hypotenuse=70.7 ft

hypotenuse=70.7

the height of the silo=oppsite side=leg2=opposite side

angle= 45 degrees

Step 2

Replace

$\begin{gathered} \text{opposite side=hypotenuse}\cdot\sin \theta \\ \text{opposite side=}70.7\text{ ft }\cdot\sin \text{ 45} \\ \text{opposite side=49.99 ft} \end{gathered}$

Round to the nearest foot,

$49.99\cong50$

so, the height of the silo is 50 ft