# Help with Law of Cosines

1. Apr 23, 2012

### theintarnets

1. The problem statement, all variables and given/known data
A ship sailing due east in the North Atlantic has been warned to change course to avoid a group of icebergs. The captain turns at point A and sails on a bearing of 62° for a while, then changes course again at point C to a bearing of 115° until the ship reaches its original course at point B. The distance between point A and B is 50 miles. How much farther did the ship have to travel to avoid the icebergs?

2. Relevant equations
a2 = b2 + c2 - 2bc*cosA
b2 = a2 + c2 - 2ac*cosB
c2 = a2 + b2 - 2ab*cosC

a/sinA = b/sinB = c/sin C

3. The attempt at a solution
I figured out all of the angles, but I only have one side, and I can't get the numbers to work in any of the law of cosines equations. I don't know if I should try law of sines, because my professor told me not to use law of sines with any angles greater than 90°. I think making a system of equations in this problem would be too complicated, I'm sure there's an easier way somewhere. Help please?

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2. Apr 23, 2012

### theintarnets

Oh! Nevermind, law of sines worked just fine. My professor is a poopyhead!