Chapter 4.3, Problem 65E

To determine

To find: the angle of elevation from the base to the top of the mountain.

Answer to Problem 65E

  $30°$

Explanation of Solution

Given:

Vertical height of mountain is 1250 feet. The distance from the top of the mountain to the base is 2500 feet.

The given data can be interpreted in the diagram form as shown below:

  

The objective here is to find the angle $\theta$ .

Now, in the right triangle ABC,

  $\begin{array}{c}\sin \theta =\frac{perpendicular}{hypotenuse}\\ =\frac{AB}{AC}\\ =\frac{1250}{2500}\\ =\frac{1}{2}\end{array}$

This gives that,

  $\begin{array}{c}\theta ={\sin }^{-1}\left(\frac{1}{2}\right)\\ \theta =30°\end{array}$