Question

A 75 feet long conveyor is used at Home Depot to unload equipment from the truck to the platform. The

Answer 1

Answer:

A. height from truck to platform = 28 ft

B.  length of the start of the conveyor to the end of the conveyor = 70 ft

C. If the height of the truck to the platform is 37.5 ft, the angle of elevation = 30°

Step-by-step explanation:

Consider the sketch of the problem attached below.

based on the laws of trigonometry, we can recall that

sin θ = $\frac{opposite side of triangle }{hypotenuse side of triangle}$

in this case, we are looking for the opposite side of the triangle.

hence we have, opposite side = 75 × sin 22

=28.095 ft ≈ 28 ft

as shown in the sketch, this opposite side is the height of the truck from hte platform

B Similarly, from the laws of trigonometry, the adjacent side of the triangle can be obtained using the relation

cos θ = $\frac{Adjacent side}{Hypotenuse side}$

Adjacent side = hypotenuse side × cos θ

Adjacent side = 75 ×cos (22)

Adjacent side = 69.53 ≈ 70 ft

C. If the new height of the truck to the platform is now 37.5 feet, the problem is redrawn in sketch 2. However, the same formulas still apply.

Sin θ = $\frac{Opposite}{Hypotenuse}$

Sin θ  = $\frac{37.5}{75}$ = 0.5

θ = $sin^{-1}$ ( 0.5)

θ = 30°