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Math Help - find the angle with the greek letter

  1. #1
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    anfield road
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    Angry find the angle with the greek letter

    in the triangle ABC, AC=3, BC=2, angleBAC=theta and angleABC=2theta
    calculate the value of theta to the nearest tenth of a degree.
    i think i'm complicating this thing for myself because i cant get farther than 2 x sin2theta = 3 x sintheta
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello the kopite
    Quote Originally Posted by the kopite View Post
    in the triangle ABC, AC=3, BC=2, angleBAC=theta and angleABC=2theta
    calculate the value of theta to the nearest tenth of a degree.
    i think i'm complicating this thing for myself because i cant get farther than 2 x sin2theta = 3 x sintheta
    OK, so now carry on:

    2\sin2\theta = 3\sin\theta

    \Rightarrow 4\sin\theta\cos\theta = 3 \sin\theta

    \Rightarrow \sin\theta = 0 or \cos\theta = \tfrac34

    \Rightarrow \theta = 41.4^o

    Grandad
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  3. #3
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    thanks a lot, but im here to understand. why does 2sin2theta equal 4sintheta x costheta in the first line of your reasoning?
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  4. #4
    Newbie darthfader's Avatar
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    I think its the 'Double Angle Identity' in Trigonometry.

    Note that

    sin 2\theta = 2sin \theta cos\theta

    I hope this helps.
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