Question

A utility pole is 40 ft tall. The pole creates a 50 ft shadow. What is the angle of elevation of the sun? Round your answer to the nearest degree. Draw the triangle. Show your work.

Answer 1

The angle of elevation of the sun is 38.65°.

Explanation:

Given a utility pole has height=40 ft and it creates a shadow of 5=ft.

Thus, in order to find the angle of elevation of the sun, let the angle of elevation of the sun be α, then

`tan{\alpha}=(AC)/(BC)`

⇒
`tan{\alpha}=(40)/(50)`

⇒
`tan{\alpha}=(4)/(5)`

⇒
`tan{\alpha}=0.8`

⇒
`{\alpha}=tan^(-1)(0.8)`

⇒
`{\alpha}=38.65^{{\circ}}`

Thus, the angle of elevation of the sun is 38.65°.