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Solve a Triangle using Trigonometry

  1. Apr 14, 2012 #1

    okh

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    1. The problem statement, all variables and given/known data
    http://img23.imageshack.us/img23/9427/imageyakj.jpg [Broken]
    AC+CB=24
    The bisector = 8.
    Find angle DCB, i.e. x.

    2. Relevant equations
    The Law of sines, I think.


    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Apr 14, 2012 #2
    You are right by guessing Law of sines. Why don't you show what work you've done till now and where exactly you're stuck?
     
  4. Apr 14, 2012 #3

    okh

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    Last edited by a moderator: May 5, 2017
  5. Apr 14, 2012 #4
    The first three equations you've written down are correct. The answer is indeed pi/5. Check your calculation again. If you still don't find your mistake, write down your step by step solution, and i'll tell you where you're going wrong.
     
    Last edited by a moderator: May 5, 2017
  6. Apr 14, 2012 #5

    okh

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    I've found my mistake, now I get 3cos^2x-sin^2x-2cosx=0 and the solution is pi/5.
    Thank you very much for helping!
     
  7. Apr 14, 2012 #6

    Curious3141

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    Homework Helper

    A word of advice, though. It's never a good idea to mix two different angle measures. Since you started in degrees, you should finish in the same. So the answer is x = 36 degrees.
     
  8. Apr 14, 2012 #7

    sharks

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    Gold Member

    I agree, with Curious3141. You might also want to justify why you rejected the other value of x, which is 108 degrees.

    I see 2 reasons:
    1. Since x is an acute angle from the figure, x cannot be 108 degrees.
    2. If you evaluate the angle CAD, using x=108 degrees, you'll get a negative value, which is not possible.

    I hope that helped you a little bit.
     
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