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Help with Law of Cosines

  1. Apr 23, 2012 #1
    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?
     

    Attached Files:

  2. jcsd
  3. Apr 23, 2012 #2
    Oh! Nevermind, law of sines worked just fine. My professor is a poopyhead!
     
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