Question

The shadow of a vertical tower is 79.0 feet long when the angle of elevation of the sun is 31.0°. Find the height of the tower. ft (Round to the nearest tenth.)

Answer 1

Answer:

47.5 ft

Explanation:

We can model the situation as follows:

So, we can relate the three given measures using the trigonometric function tangent as:

$\tan 31=\frac{x}{79}$

Therefore, the value of x is:

$\begin{gathered} 79^{}\cdot\tan 31=79\cdot\frac{x}{79} \\ 79\cdot\tan 31=x \\ 79\cdot(0.6)=x \\ 47.5=x \end{gathered}$

Therefore, the height of the tower is 47.5 ft