Chapter 4.8, Problem 26E

a.

To determine

To find: The height of the steeple $\text{CD}$ .

Answer to Problem 26E

Determine $\text{AD}$ and $\text{AC}$

Explanation of Solution

Given information: Angles ${37}^{\circ }$ and ${49}^{\circ }40^{\prime }$ ,

And base length $\text{= 50 ft}\text{.}$

Calculation:

Consider, the figure,

  

Here,

  $\angle ABD={37}^{\circ }$

  $\angle ABC={49}^{\circ }40^{\prime }$

And $AB=50\text{ ft}.$

At, first we determine $AD$ and $AC$

b.

To determine

To find: The height of the steeple $CD$ .

Answer to Problem 26E

  $\text{AD = 37}\text{.68 ft}\text{.}$

  $AC\simeq 58.89\text{ ft}.$

Explanation of Solution

Given information: Angles ${37}^{\circ }$ and ${49}^{\circ }40^{\prime }$ ,

And base length $\text{= 50 ft}\text{.}$

Calculation:

  

  $\begin{array}{l}\tan \angle ABD=\frac{AD}{AB}\\ \Rightarrow AD=AB\times \tan \angle ABD\\ \Rightarrow AD=50\times \tan {37}^{\circ }\\ \Rightarrow AD=37.68\text{ ft}\text{.}\end{array}$

Again

  $\begin{array}{l}\tan \angle ABC=\frac{AC}{AB}\\ \Rightarrow AC=AB\times \tan \angle ABC\\ \Rightarrow AC=50\times \tan {49}^{\circ }40^{\prime }\\ \Rightarrow AC=50\times \tan {\left(49+\frac{40}{60}\right)}^{\circ }\\ \Rightarrow AC=50\times \tan {\frac{149}{3}}^{\circ }\\ \Rightarrow AC\simeq 58.89\text{ ft}\text{.}\end{array}$

c.

To determine

To find: The height of the steeple $CD$ .

Answer to Problem 26E

The height is $\text{21}\text{.21 ft}\text{.}$

Explanation of Solution

Given information: Angles ${37}^{\circ }$ and ${49}^{\circ }40^{\prime }$ ,

And base length $\text{= 50 ft}\text{.}$

Calculation:

  

Here,

The height of the steeple is

  $\begin{array}{l}CD=AC-AD\\ \Rightarrow CD\simeq 58.89-37.68\text{ ft}.\\ \Rightarrow CD\simeq 21.21\text{ ft}\text{.}\end{array}$

Hence, the height is $21.21\text{ ft}.$