Solving for Distance using Law of Cosines

[theintarnets]

Homework Statement

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?

Homework Equations

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

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

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?

 

[theintarnets]

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