Chapter 12.8, Problem 2P

To determine

Find the time after which she will be exactly be southeast of where she started.

Answer to Problem 2P

About 1.5 hours.

Explanation of Solution

Given:

J is flying a plane on a triangular course at 320 mi/h.She flies due east for two hours and then turns right through a $65°$ angle.

Formula Used:

Law of Sine:

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

  

Calculation:

J flies towards East at 320 mi/h , so , distance she travelled after 2 hours = 320(2) = 640 mi

The angle to the Southeast , from where she started is $45°$

The third angle of the triangle = $180°-65°-45°=70°$

Represent the situation :

  

Use Law of Sine:

  $\begin{array}{l}\frac{x}{\sin 45°}=\frac{640}{\sin 70°}\\ \Rightarrow x=\sin 45°\cdot \frac{640}{\sin 70°}\mathrm{.................}[\text{multiply each side by }\sin 45°]\\ \Rightarrow x\approx 481.6\end{array}$

Since the speed is 320 mi/h , so the time = $\frac{dis\tan ce}{speed}=\frac{481.6}{320}\approx 1.5$

So, time after which she will be exactly be southeast of where she started is about 1.5 hours.