SOLUTION: 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

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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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F44000
Cos(C) = .7136
ArcCos = 44.47 degree, therefore
180 - 44.47 = 135.5 degree turn to head towards Island B