Mark M. answered • 07/27/15

Mathematics Teacher - NCLB Highly Qualified

Draw and label a diagram:

Mark the starting point as A. Draw a line due west (to the left) ending at point B.

The plane changes direction to 190°. This is measured from due North. This results in an angle at B of 100° from AB.

The plan is traveling South by West.

Draw a line from B at this angle ending at C. Connect AC.

Using the Law of Cosines:

AC

^{2}= AB^{2}+ BC^{2}- 2(AB)(BC)cos B.AC

^{2}= 14400 + 57600 - 57600 cos 100°AC

^{2 }= 72000 - 57600(-0.173648178)AC

^{2}≈ 72000 + 10002AC

^{2}≈ 82002AC ≈ 286.359913