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Math Help - reciprocal form Of law of sines . question

  1. #1
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    reciprocal form Of law of sines . question

    Hello i am a bit confused when it comes to this law.

    How do i know when the reciprocal form is to be used
    And how do i know when its not to be used?

    If anyone could make an example.

    Thanks
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  2. #2
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    Re: reciprocal form Of law of sines . question

    Quote Originally Posted by Riazy View Post
    Hello i am a bit confused when it comes to this law.

    How do i know when the reciprocal form is to be used
    And how do i know when its not to be used?

    If anyone could make an example.

    Thanks
    The two forms are equivalent. The non-reciprocal form nicely equals the diameter of the circle circumscribing the triangle.

    I can see using one or the other to try and keep very small numbers out of the denominator when doing things numerically.
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  3. #3
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    Re: reciprocal form Of law of sines . question

    Hello, Riazy!

    It really doesn't matter which form you use.

    . . \frac{a}{\sin A} \,=\,\frac{b}{\sin B}\,=\,\frac{c}{\sin C}\,\text{ is equivalent to }\,\frac{\sin A}{a} \,=\,\frac{\sin B}{b} \,=\,\frac{\sin C}{c}


    However, depending on what you are seeking,
    . . there is a more convenient choice.


    Example: . b = 7,\:A = 50^o,\:B = 60^o.\;\text{ Find }a.

    Since we want a, I would choose the form with a on top.

    . . \frac{a}{\sin A} \,=\,\frac{b}{\sin B} \quad\Rightarrow\quad \frac{a}{\sin50^o} \,=\,\frac{7}{\sin60^o} \quad\Rightarrow\quad a \,=\,\frac{7\sin50^o}{\sin60^o}\;\text{ . . . etc.}
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