__Category__: Trigonometry"Published in Newark, California, USA"

A pilot flew in the direction of 140° from A to B and then in the direction of 240° from B to C. A is 500 miles from B and 800 miles from C. Find the distance of the last flight and the direction from A to C.

__Solution__:

The first thing that we have to do is to analyze the problem very well. The given angles are expressed as course. Typically course is measured in degrees from 0° clockwise to 360° in compass convention (0° being north, 90° being east).

Let's draw the figure to analyze the given word problem as follows

Photo by Math Principles in Everyday Life |

Complete further the labeling of the above figure as follows

Photo by Math Principles in Everyday Life |

Next, use Cosine Law to solve for the distance of the last flight from A to C

Therefore, the distance of the last flight from A to C is

**1,040.0154 miles**.

Finally, use Sine Law to solve for the direction of the last flight from A to C

or

Therefore, the direction of the last flight from A to C is 140° + 49°14'50" =

**189°14'50"**.