Chapter 8.5, Problem 29WE

To determine

To find: the length of $BT$ .

Answer to Problem 29WE

The length of $BT$ is $135.7624\text{ ft}\text{.}$

Explanation of Solution

Given:

The triangles with dimensions are shown below:

  

Calculation:

In triangle $WBH$ ,

  $\begin{array}{l}\tan 37°=\frac{BH}{HW}\\ \Rightarrow HW=\frac{BH}{\tan 37°}\mathrm{...}(1)\end{array}$

Again, in triangle $WHT,$

  $\begin{array}{l}\tan 61°=\frac{HT}{HW}\\ \Rightarrow HT=HW\tan 61°\mathrm{...}(2)\end{array}$

Now, from the equation − (1) and (2), we have:

  $HT=BH\frac{\tan 61°}{\tan 37°}$ .

Now, to find the value of $BT,$ we use the following fact:

  $BT=BH+HT.$

But, since $HT=BH\frac{\tan 61°}{\tan 37°}$ , we get:

  $BT=BH+BH\frac{\tan 61°}{\tan 37°}.$

  $\Rightarrow$$BT=BH\left(1+\frac{\tan 61°}{\tan 37°}\right)=40\left(1+\frac{1.80405}{0.75355}\right).$

  $\Rightarrow$$BT=40\left(1+\text{2}\text{.39406}\right)=40\times 3.39406=135.7624\text{ ft}\text{.}$

Hence, the length of $BT$ is $135.7624\text{ ft}$ . Therefore, $T$ is $135.7624\text{ ft}$ above the street level.