Question

Find the measure of a. Please help me as soon as you can, Thank you.

Answer 1

If you know the length of two sides and the measure of the angle between them, you can find the third side using the law of cosines: if $b$ and $c$ are known, and so is the angle $\alpha$ between them, the remaining side $a$ is given by

$a^2 = b^2+c^2-2bc\cos(\alpha)$

So, in your case, the expression becomes

$a^2 = 64+121-2\cdot 8\cdot 11\cdot \cos(32.2) =36.07$

This means that we can deduce the value for a by squaring both sides (we're not considering both signs of the root because it makes no sense to have a negative length:

$a = sqrt{36.07} \approx 6$