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Thread: In order to apply the law of cosines to find the measure of an interior angle...

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    In order to apply the law of cosines to find the measure of an interior angle...

    In order to apply the law of cosines to find the measure of an interior angle, it is enough to know which of the following?

    A. The area of the triangle

    B. The length of all three sides of a triangle

    C. At least two of the angles of a triangle and the length of one of its sides

    Please explain. Thank you!
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    Re: In order to apply the law of cosines to find the measure of an interior angle...

    A. The area of the triangle isn't enough to find an interior angle, you would still need the two sides that surround it, so you can use $\displaystyle \begin{align*} A = \frac{1}{2}\,a\,b\sin{(C)} \end{align*}$.

    B. Yes if you have all three sides of the triangle, you can use the cosine rule: $\displaystyle \begin{align*} \cos{(C)} = \frac{a^2 + b^2 - c^2}{2\,a\,b} \end{align*}$.

    C. You would use the sine rule instead. If you have any two angles, you can always find the third because they add up to $\displaystyle \begin{align*} 180^{\circ} \end{align*}$, and then you can use the Sine Rule to find the remaining sides.
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