Chapter 12.5, Problem 10P

To determine

Find the length of the tent in the bottom.

Answer to Problem 10P

294 cm

Explanation of Solution

Given:

A camping tent is supported by a rope stretched between two trees at a height of 210 cm.The sides of the tent make an angle of $55°$ with the level ground.

Formula Used:

  $\tan \theta =\frac{\text{length of opposite side to }\theta }{\text{length of adjacent side to }\theta }$

Calculation:

Represent the given situation

  

We need to find x and length of the tent at the bottom is 2x .

Use the tan formula :

  $\begin{array}{l}\tan 55°=\frac{\text{length of opposite side to 55}°}{\text{length of adjacent side to 55}°}\\ \Rightarrow \tan 55°=\frac{210}{x}\\ \Rightarrow x=\frac{210}{\tan 55°}\mathrm{.........................}[\text{multiply each side by }\frac{x}{\tan 55°}]\\ \Rightarrow x\approx 147\\ \Rightarrow 2x=2\cdot 147=294\end{array}$

So, the length of the bottom of the tent is 294 cm.