# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 6, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Given $a = 4$, $b = 6$, and $C = \frac{5 \pi}{12}$, we can calculate side $c$:
$c = \sqrt{{a}^{2} + {b}^{2} - 2 a b \cos \left(C\right)}$
$c = \sqrt{{4}^{2} + {6}^{2} - 2 \left(4\right) \left(6\right) \cos \left(\frac{5 \pi}{12}\right)}$
$c \approx 6.291$