Question 1089625
Island A is 160 miles from island B. A ship captain travels 220 miles from island A and then finds that he is off course and 200 miles from island B.
 What bearing should he turn to, so he is heading straight towards island B?
: 
Draw this out as a triangle ABC where A & B are the islands and C it the point that the ship changes it's heading towards B
 Use the law of cosines; c^2 = a^2 + b^2 - 2(ab)Cos(C), where
a = 200
b = 220
c = 160
Arrange as
2(ab)Cos(C) = a^2 + b^2 - c^2 
2(200*220)Cos(C) = 200^2 + 220^2 - 160^2
2(44000)Cos(C) = 40000 + 48400 - 25600
2(44000)Cos(C) = 62800
Simplify, divide both sides by 2
44000*Cos(C) = 31400
Cos(C) = {{{31400/44000}}}
Cos(C) = .7136
ArcCos = 44.47 degree, therefore
180 - 44.47 = 135.5 degree turn to head towards Island B