AMC 12 Mock Exam 2 Problem 11

Since $A$ and $B$ are acute, $\cos A=\frac45$ and $\cos B=\frac{12}{13}$. Because $C=\pi-(A+B)$, $$\cos C=-\cos(A+B)=\sin A\sin B-\cos A\cos B=\frac{15}{65}-\frac{48}{65}=\boxed{-\tfrac{33}{65}}.$$ (So $C$ is obtuse. The distractors $-\frac{63}{65}$ and $\frac{16}{65}$ are $-\cos(A-B)$ and $\sin(A-B)$.)