Chapter 8.5, Problem 28STP

To determine

To select:

The correct option to show the height of cell-phone tower:

A. $52$

B. $110$

C. $63$

D. $115$

Answer to Problem 28STP

The correct option is D. The height of cell-phone tower is $115ft$

Explanation of Solution

Given information:

The base length: $80$

Angle of elevation: $54°$

The height of Ryan: $5ft$

Calculation:

Consider,

The net vertical distance: $x$

The horizontal distance is $80ft$ , and the angle of elevation is $54°$ .

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 $\angle A$ .

As per the definition of tangent, the height of cell-phone tower is calculated as:

  $\begin{array}{l}\tan 54°=\frac{x}{84}\\ 84\tan 54°=x\\ x\approx 110ft\end{array}$

Here, the height of Ryan is $5ft$ . So, height of cell-phone tower is given by:

  $\begin{array}{l}h=110ft+5ft\\ h=115ft\end{array}$

So, height of cell-phone tower calculated as $h=115ft$ . Therefore, correct option is D.