Question

A pilot 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.

Answer 1

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