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Cosine rule

  1. Jan 5, 2016 #1
    1. The problem statement, all variables and given/known data
    In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x?

    2. Relevant equations
    I used the cosine rule here

    3. The attempt at a solution
    As we have 2 sides and an angle I used the cosine rule - Am I correct?
    (2) means squared

    b(2) = a(2) + c(2) - 2ac cos B
    so
    x(2) =21(2) + (2x)(2) - 2.21.2x.c cos B
    x(2) =441 + 4x(2) - 84x cos B
    3x(2) = 84x cosB - 441

    How do I find x from here?
     
  2. jcsd
  3. Jan 5, 2016 #2

    Merlin3189

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    Gold Member

    Why did you choose to use angle B ?
    Since you know angle A, wouldn't that be easier?
     
  4. Jan 5, 2016 #3

    Samy_A

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    Applying the cosine rule is the way to go.
    But you should apply it correctly, with the angle you know (that's angle A):
    ##a²=b²+c²-2bc\cos(A)##, where a is the side opposite angle A, b the side opposite angle B and c the side opposite angle C.
    You also know ##\cos(A)=\cos(120°)##.
     
    Last edited: Jan 5, 2016
  5. Jan 5, 2016 #4
    Thanks everyone, I have found that x(2) = 63 which makes x = 7.94 cm (to 2dp) using the cosine rule

    Am I correct?

    a(2) = b(2) + c(2) - 2bc cos B
    so
    21(2) =x(2) + (2x)(2) - 2.x.2x cos B
    441 = 5x(2) - 4x(2) cos 120
    441 = x(2) (5-4 cos 120)
    x(2) = 441 / (5-4cos 120)
    x(2) = 63
    x = 7.94 cm (to 2dp)
     
  6. Jan 5, 2016 #5

    Samy_A

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    Looks correct (except that the angle should better be called A, not B).
     
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