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

47.5 ft

Step-by-step explanation:

We can model the situation as follows:

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

`\tan 31=(x)/(79)`

Therefore, the value of x is:

`\begin{gathered} 79^{}\cdot\tan 31=79\cdot(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