Chapter 8.5, Problem 21PPS

To determine

To calculate:

The angle of elevation and depression

Answer to Problem 21PPS

The angle of elevation and depression are $4.71°$ and $2.02°$ respectively.

Explanation of Solution

Given information:

Length from base to peak: $1200m$

Calculation:

J is taller than the target. Thus, J throws the dart at an angle of depression.

The side opposite the angle of depression is $6-5.7=0.3ft$

Consider,

The angle of depression: $x$

As per Alternate Interior Angles Theorem the angle of depression and the angle of elevation are congruent.

Let’s draw a figure to represent the given information:

  

If is a $△ABC$ right triangle with acute $\angle A$ , then the tangent of $\angle A$ is the ratio of the length of

leg opposite $\angle A$ to the length of the leg adjacent $\angle A$ .

The angle of depression is calculated as:

  $\begin{array}{l}\sin x°=\frac{0.3}{8.5}\\ x°={\sin }^{-1}\left(\frac{0.3}{8.5}\right)\\ x=2.02°\end{array}$

K is shorter than the target. Thus, K throws the dart at an angle of elevation.

The side opposite the angle of depression is $5.7-5.0=0.7ft$

Consider,

The angle of elevation: $y$

Let’s draw a figure to represent the given information:

  

The angle of elevation is calculated as:

  $\begin{array}{l}\sin y°=\frac{0.7}{8.5}\\ y°={\sin }^{-1}\left(\frac{0.7}{8.5}\right)\\ y=4.71°\end{array}$