Chapter 8.5, Problem 19PPS

(a)

To determine

To calculate:

The angle of elevation to Mount Whitney

Answer to Problem 19PPS

The angle of elevation to Mount Whitney is $154.9ft$

Explanation of Solution

Given information:

Length from base to peak: $1200m$

Calculation:

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 elevation to Mount Whitney is calculated as:

  $\begin{array}{l}\tan x°=\frac{4421}{1200}\\ x°={\tan }^{-1}\left(\frac{4421}{1200}\right)\\ x=74.81°\end{array}$

(b)

To determine

To calculate:

The horizontal distance from sea level

Answer to Problem 19PPS

The horizontal distance from sea level is $110.1m$

Explanation of Solution

Given information:

Depression angle: $38°$

Calculation:

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 horizontal distance from sea level is calculated as:

  $\begin{array}{l}\tan 38°=\frac{86}{x}\\ x=\frac{86}{\tan 38°}\\ x=110.1m\end{array}$