Chapter 7.3, Problem 8CYU

To determine

To find: the height of the tower.

Answer to Problem 8CYU

  $\Delta QVS=\Delta RTS$ , $VS=20$ .

Explanation of Solution

Given:

The shadow of a cell-phone tower is 100 foot.

At that time, the shadow of a 4 foot-6inch post is 3 feet 4 inch.

Calculation:

According to the question, both the triangles are similar, therefore

  $\begin{array}{l}\frac{\text{height of the tower}}{\text{length of the tower's shadow}}=\frac{\text{height of the post}}{\text{length of the post's shadow}}\\ \Rightarrow \frac{\text{height of the tower}}{\text{100}}=\frac{4\frac{6}{12}}{3\frac{1}{3}}\left\{\text{substitutes these value}\right\}\\ \therefore \frac{h}{100}=\frac{\frac{9}{2}}{\frac{10}{3}}\\ \Rightarrow h=100\times \frac{9}{2}\times \frac{3}{10}\\ \therefore h=135ft\end{array}$

Hence, the height of the tower is $h=135ft$ .