Question

3. A utility pole is 38 ft tall. The pole creates a 53 ft shadow. What is the angle of elevation of the sun? Round your answer to the nearest degree. Show your work

Answer 1

The angle of elevation of the sun is
`36\degree`.

Explanation:

Let
`x` be the angle of elevation of the sun as shown in the diagram.

Then the side length which is
`38` feet is opposite to
`x` and the side length which is
`53` feet is adjacent to
`x`.

Therefore we use the trigonometric ratio that involves the opposite and adjacent sides, which is the tangent ratio.

`\tan x=(38)/(53)`

`\Rightarrow \tan x=0.71698`

We solve for
`x` to get,

`x=\arctan (0.71698)`

`\Rightarrow x=35.63981`

To the nearest degree, the angle of elevation is
`36\degree`