Chapter 8.4, Problem 45E

To determine

To find: the height of pole and length of cable to the nearest tenth of a meter.

Answer to Problem 45E

  $\begin{array}{l}h=13.1\text{ m}\\ l=13.7\text{ m}\end{array}$

Explanation of Solution

Given information:

The figure for the given situation is as follows:

  

The angle between cable and ground $\left(\theta \right)$ is $73°$ .

Height of pole $=h$

Length of cable $=l$

Distance of cable from base, $b=4$

Calculation:

The height of the pole can be evaluated as follows:

  $\begin{array}{c}\tan \theta =\frac{h}{b}\\ \tan 73°=\frac{h}{4}\\ h=4\left(\tan 73°\right)\\ =13.1\text{ m}\end{array}$

The length of the cable can be evaluated as follows:

  $\begin{array}{c}\cos \theta =\frac{b}{l}\\ \cos 73°=\frac{4}{l}\\ l=\frac{4}{\cos 73°}\\ =13.7\text{ m}\end{array}$

Thus, the height of pole is 13.1 m and length of cable is 13.7 m.