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Math Help - Sine Law and Cosine Law

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    Sine Law and Cosine Law

    hey, I was just wondering when i would use sine law, opposed to cosine law and vice-versa.

    Thanks!
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    Member Jonboy's Avatar
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    You don't mean Law of Sines and Law of Cosines, right?


    If you mean the law of sine, that is: Sin\,\theta = \frac{opp}{hyp}

    And the law of cosine: Cos\,\theta = \frac{adj}{hyp}

    Then you can use use either of them when you have a right triangle.

    Which one depends on what you know, be it the opposite side, adjacent side, or the hypotenuse.
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jays-9 View Post
    hey, I was just wondering when i would use sine law, opposed to cosine law and vice-versa.

    Thanks!
    You use the law of sines when you have two known angles and one known side in a triangle (AAS, ASA).

    Law of Sines: \frac{\sin(\alpha)}{A}=\frac{\sin(\beta)}{B}=\frac  {\sin(\gamma)}{C}

    You use the law of cosines when you have two known sides and one known angle (triangle is SAS).

    \begin{aligned}<br />
\text{Law of Cosines: }&A^2=B^2+C^2-2BC\cos(\alpha) \\<br />
&B^2=A^2+C^2-2AC\cos(\beta) \\<br />
&C^2=A^2+B^2-2AB\cos(\gamma)<br />
\end{aligned}
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