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Math Help - Triangles with trigonometry

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    Triangles with trigonometry

    If A is an obtuse angle in a triangle and sin A = 5/13, calculate the exact value of sin 2A.

    I do not know how to go about this question. All I have done is found that the reference angle is about 22.6 degrees, but I have to find the exact value, how do I solve this?
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    Quote Originally Posted by bhuang View Post
    If A is an obtuse angle in a triangle and sin A = 5/13, calculate the exact value of sin 2A.

    I do not know how to go about this question. All I have done is found that the reference angle is about 22.6 degrees, but I have to find the exact value, how do I solve this?
    since A is obtuse, \cos{A} = -\frac{12}{13}

    \sin(2A) = 2\sin{A}\cos{A}
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    how did you get the ratio for cosine?
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    Quote Originally Posted by bhuang View Post
    how did you get the ratio for cosine?
    I sketched a reference triangle in quad II ...

    since \sin{A} = \frac{5}{13} , opposite side = 5 , hypotenuse = 13

    using Pythagoras ... adjacent side = -12

    \cos{A} = -\frac{12}{13}
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