Chapter 4.8, Problem 26E

To determine

To calculate: The angle of depression.

Answer to Problem 26E

Angle of depression is $\theta ={1.996}^{\circ }$

Explanation of Solution

Given information:

Length of cellular telephone tower is $120\text{ feet}$ . The tower is placed on top of a mountain that is 1200 feet above sea level. The cell phone user is 5 miles horizontally away and 400 feet above sea level.

The objective is to find angle of depression.

According to the given information, the diagram can be drawn as,

  

Now, from the diagram

  $\begin{array}{c}\tan \theta =\frac{120+1200-400}{26400}\\ =\frac{920}{26400}\\ \theta ={\tan }^{-1}\left(\frac{92}{2640}\right)\\ ={1.996}^{\circ }\end{array}$

Therefore, the angle of depression is $\theta ={1.996}^{\circ }$