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

Answer:

The angle of elevation of the sun is 38.65°.

Step-by-step 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

$tan{\alpha}=\frac{AC}{BC}$

⇒$tan{\alpha}=\frac{40}{50}$

⇒$tan{\alpha}=\frac{4}{5}$

⇒$tan{\alpha}=0.8$

⇒${\alpha}=tan^{-1}(0.8)$

⇒${\alpha}=38.65^{{\circ}}$

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