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Math Help - Laws Of Sine

  1. #1
    Member >_<SHY_GUY>_<'s Avatar
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    Question Laws Of Sine

    i have one quick question...

    a problem gives us that:

    A= 60 degrees, a=9, c = 10...
    my only concern is that if the remaining two angles are also 60...
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  2. #2
    Member Jonboy's Avatar
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    you can't just assume that. you can assume though that the other two angles will add up to 120 degrees though.

    Use Law of Sines:

    \frac{Sin 60}{9}=\frac{Sin C}{10}

    \frac{\frac{\sqrt{3}}{2}}{9}=\frac{Sin C}{10}

    Criss-Cross multiply: 9SinC = \frac{10\sqrt{3}}{2} = 5\sqrt{3}

    So: SinC =  \frac{5\sqrt{3}}{9}

    We need the angle, so we use inverse Sin ( Sin^{ - 1}).

    C = Sin^{ - 1} (\frac{5\sqrt{3}}{9}) \approx 74.21^o

    The other angle is approximately 120 - 74.21 = 45.79^o
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