Chapter 8.7, Problem 7CE

To determine

the approximate angle of depression and show why it is an approximate angle.

Answer to Problem 7CE

The approximate angle of depression is $23°$ .

Explanation of Solution

Given:

The distance from A to B is 130 m and the vertical descent of AC is 50 m.

Calculation:

Assume the angle of depression is $\theta$ .

By the ratio of sides from a right − angled triangle, we can write:

  $\begin{array}{l}\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}},\\ \Rightarrow \sin x=\frac{50\text{ m}}{130\text{ m}},\\ \Rightarrow x=23°.\end{array}$

Hence, the answer is approximate since the steepness of hill varies and the angle of depression measures the hill’s steepness.