Question

A ship travels due west for 60 miles. It then travels in a northwest direction for 85 miles and ends up 119 miles from its original position. To the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? Show your work.

Answer 1

Given:
due west: 60 miles
northwest: 85 miles
original point to destination point: 119 miles

Let us use the Law of Cosines to find the angle.

119² = 60² + 85² - [(2*60*85)*cos(x)]
14,161 = 3600 + 7225 - (10,200 * cos(x))
14,161 = 10,825 - 10,200 cos(x)
14,161 - 10,825 = -10,200 cos(x)
3.336 = -10,200 cos(x)
3,336 / -10,200 = cos(x)
-0.3271 = cos(x)
-0.3271 / cos = x
cos^-1 (-0.3271) = x
109.09 = x

109.09° or 109.10° north of west.