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

Answer:

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

Step-by-step 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.

$\tan x=\frac{38}{53}$

$\Rightarrow \tan x=0.71698$

We solve for $x$ to get,

$x=\arctan (0.71698)$

$\Rightarrow x=35.63981$

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