Chapter 14, Problem 1CT

To determine

To find:The distance and the bearing of each from the other to the nearest degree

Answer to Problem 1CT

The distance is 461 km and the bearing of each from the other to the nearest degree is 55.

Explanation of Solution

Given:

The headings are 165 and 220.

Calculation:

Both travels at 250 km/h and after 2 hours they made 500 km.

The angle formed is,

  $220°-165°=55°$

The distance is calculated using the law of cosine.

  $\begin{array}{c}{c}^2=a^2+b^2-2ab\cos \alpha \\ c=\sqrt{{\left(500\right)}^2+{\left(500\right)}^2+2\left({\left(500\right)}^2\cos 55\right)}\\ =461\text{ km}\end{array}$

Thus, the distance is 461 km and the bearing of each from the other to the nearest degree is 55.