Question

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Can someone help me! It's Law of Cosines, and I'm having to use the formula $a^{2} + b^{2} -2ab Cos(C)=c^{2}$ but I do not know which side length is a, b and c. In the last question, I was given the angles and that's how I figured out which side length is which. All I'm given is two side lengths and an unlabeled angle. So please help me someone!

Answer 1

You use the law of cosines whenever you're given a SAS triangle. The formula is

$c^2=a^2+b^2-2ab\cos C$

C is the given angle, c is the side opposite this angle, and a/b are the given sides adjacent to angle C.

In this case, if $c$ is the length of the missing side, then

$c^2=9^2+6^2-2\cdot9\cdot6\cos37^\circ\implies c\approx7.66$