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 [tex] b [/tex] and [tex] c [/tex] are known, and so is the angle [tex] \alpha [/tex] between them, the remaining side [tex] a [/tex] is given by
[tex] a^2 = b^2+c^2-2bc\cos(\alpha) [/tex]
So, in your case, the expression becomes
[tex] a^2 = 64+121-2\cdot 8\cdot 11\cdot \cos(32.2) =36.07 [/tex]
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:
[tex] a = sqrt{36.07} \approx 6 [/tex]
