Find Angle C?

A plane flies from city A to city B, a distance of 150 miles and then turns through an angle 40 degrees and heads toward city C, a distance of 169 miles. Through what angle C should the pilot turn at city C (which is angle C) to return to city A?





NOTE: The distance from city A to city C = 300 miles.

Find Angle C?
The plane's movement forms a triangle ABC. AB = 150, BC = 169, AC = 300 as given.





You know the angle %26lt;ABC is 140 degrees (as the plane turned 40 degrees from a straight angle to go to C). Therefore, it's simple use of the Sine Rule to find the angle %26lt;BCA.





Sin140/300 = SinX/150


SinX = (Sin140)/2...


I don't have a calculator, but 360-X should give you the angle you need, according to my diagram. (The angle X is the acute angle %26lt;BCA but realistically the plane would have to turn through the larger angle.)