Question

Help! Will give a Medal!!!

Answer 1

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? Show your work.

Answer 2

Set it up as triangle ABC, where side A is 83, B is 111, and C is 165. Use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

We are looking for the angle opposite side c; this is angle C. Substitute your known values and solve:

165^2 = 83^2 + 111^2 - 2(83)(111) cos(C)
27225 = 6889 + 12321 - (18426 * cos(C))
27225 = 19210 - (18426 * cos(C))
27225 + (18426*cos(C)) = 19210
18426(cos(C)) = -8015
cos(C) = -0.43
cos^-1(-0.43) = 115.8

This is the heading when it turned; 115.8 degrees. Subtract this from 180 (the heading at which it was originally directed) to get 64.2 degrees. This is how many degrees it turned.

Answer 3

Thanks so much!