Chapter 4.8, Problem 21E

To determine

Tofind:The height of the steeple of a church if the angle of elevation to the bottom of the steeple and top of the steeple are $35°$ and $48°$ , respectively from a point that is 50 feet far from the base of the church.

Answer to Problem 21E

The height of the steeple of the churchis $20.5$ feet.

Explanation of Solution

Given information:

The angle of elevation to the bottom of the steeple and top of the steeple are $35°$ and $48°$ from a point that is 50 feet far from the base of the church.

Calculation:

Let’s theheight of the church is $\text{BC}$ and the height of the steeple is $\text{CD}$ . The distance between the point and the base of the church is AB. The height of the steeple is the difference between BD and BC.

  

In $\Delta \text{DAB}$ , calculate the length of BD.

  $\begin{array}{c}\tan 35°=\frac{\text{BD}}{50}\\ \text{BD}=50\cdot \tan 35°\\ =35\text{feet}\end{array}$

In $\Delta \text{CAB}$ , calculate the length of BC.

  $\begin{array}{c}\tan 48°=\frac{\text{BC}}{50}\\ \text{BC}=50\cdot \tan 48°\\ =55.5\text{feet}\end{array}$

Subtract the value of BD from BC to calculate the height of the steeple $h$ .

  $\begin{array}{c}\text{CD}=\text{BC}-\text{BD}\\ h=55.5-35\\ \approx 20.5\text{feet}\end{array}$

Therefore, the height of the steeple of the church is $20.5$ feet.