Apilot flies a plane due west from 150 miles, then turns 42 degrees north of west for 70 miles. find the planes resultant distance and direction from the starting point.

This can be solve using cosine lawbut first let as solve the included angle in the triangle form
angle = 180 - 42angle = 138
c^2 = a^2 + b^2 - 2ab(cos angle)c^2 = 150^2 + 70^2 - 2(150)(70)cos(138)C^2 = 43006.04c = sqrt(43006.04)c = 207.37 mile
directionsin (x) / 70 = sin (138)/ 207.37sin x = 0.2259x = arcsin(0.2259)x = 13.05 degree north of west