A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 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?

We first determine the angle between the 83 mi and the 111 mi sides. Let this angle be represented by x, and use the cosine law to solve this:
165^2 = 83^2 + 111^2 - 2(83)(111)cos(x)
cos(x) = 115.8 degrees
Therefore, the angle north of west that the ship turned would be 180 - 115.8 = 64.2 degrees.