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Math Help - Show that b=3c

  1. #1
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    Show that b=3c

    Triangle\: ABC\: with\: A=60

    if\: \sin A=\sqrt 7 \sin C

    show that b=3c.
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  2. #2
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    Quote Originally Posted by razemsoft21 View Post
    Triangle\: ABC\: with\: A=60

    if\: \sin A=\sqrt 7 \sin C

    show that b=3c.
    A=60, sin A= \frac{\sqrt3}{2}

    sin C= \frac{sin A}{\sqrt 7}

    sin C= \frac{\sqrt 3}{2 * \sqrt 7}

    sin C= \frac{\sqrt 21}{14}

    from here, work out cos C

    cos C = \frac{5*\sqrt 7}{14} (I am taking cos C to be positive,
    otherwise angle B would come out reflex)


    since A+B+C = 180, B=180-(A+C), sin B=sin (A+C)=sin A * cos C + cos A * sin C

    = \frac{3*\sqrt 21} {14}


    Now use sine rule in the triangle ABC, you will get b=3c
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  3. #3
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    Nice job, thanks a lot
    b=3c
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