This case can be solved via the Law of cosines, which applies exactly to this problem:
Suppose you know two sides [tex] a [/tex] and [tex] b [/tex] of a triangle, and the angle [tex] \alpha [/tex] between them.
Then, the third side [tex] c [/tex] satisfies the following equation:
[tex] c^2 = a^2+b^2-2ab\cos(\alpha) [/tex]
In our case, the equation becomes
[tex] c^2 = 8^2+11^2-2\cdot 8 \cdot 11\cos(32.2^\circ) [/tex]
We can simplify the expression:
[tex] c^2 \approx 64+121-176\cdot 0.85 = 185 - 149.6 = 35.4 [/tex]
So, we have
[tex] c^2 \approx 35.4 \implies c \approx \sqrt{35.4} \approx 6[/tex]
