Chapter 6.2, Problem 52E

To determine

To Find: The height of communication tower.

Answer to Problem 52E

The height of communication tower is $543.78\text{ft}$.

Explanation of Solution

Given:

The length of guy wire is $600\text{ft}$.

Angle between wire and ground is $65°$.

Calculation:

The below figure show the angle between tower and wire.

Figure (1)

Let $h$ is the height of the communication tower.

Consider the above figure (1) to calculate the value of $h$.

Formula Used: Trigonometry property of sine.

$\text{sin}\theta =\left(\frac{\text{opposite}}{\text{hypotenuse}}\right)$

Use sine property of trigonometry to calculate the value of $h$.

Substitute $65°$ for $\theta$, $h$ for opposite and $600\text{ft}$ for hypotenuse.

$\begin{array}{c}\text{sin65}°=\left(\frac{h}{600}\right)\\ h=\left(\text{sin65}°\times 600\right)\\ =\left(0.9063\times 600\right)\left(\because \text{sin65}°=0.9063\right)\\ h\approx 543.78\text{ft}\end{array}$

Therefore, the height of the communication tower is $543.78\text{ft}$.