Chapter 8.5, Problem 18PPS

To determine

To calculate:

The width of the field

Answer to Problem 18PPS

The width of the field is $154.9ft$

Explanation of Solution

Given information:

Height of balloon: $800ft$

Angle of depression on the farther side: $27°$

Angle of depression on the closets side: $32°$

Calculation:

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

Consider, the width of the field is $xft$

  

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 $\angle A$ .

Calculate $AH$ :

  $\begin{array}{l}\tan 32°=\frac{800}{AH}\\ AH=\frac{800}{\tan 32°}\\ AH\approx 1280.3ft\end{array}$

The width of the field is calculated as:

  $\begin{array}{l}\tan 27°=\frac{800}{GH}\\ GA+AH=\frac{800}{\tan 27°}\\ x+1280.3=\frac{800}{\tan 27°}\\ x=1570.1-1280.3\\ x=289.8ft\end{array}$