Answer
$C = 92.2^{\circ}$
Work Step by Step
We can try to use the law of cosines to find $C$:
$c^2 = a^2+b^2-2ab~cos~C$
$2ab~cos~C = a^2+b^2-c^2$
$cos~C = \frac{a^2+b^2-c^2}{2ab}$
$cos~C = \frac{13^2+7^2-15^2}{(2)(13)(7)}$
$cos~C = -0.03846$
$C = arccos(-0.03846)$
$C = 92.2^{\circ}$
