In triangle ABC, sides a = 8 and b = 15 include an angle C = 60°. What is the length of side c?

Two sides and the included angle are known, so use the Law of Cosines: $c^2=a^2+b^2-2ab\cos C=64+225-2(8)(15)\cos60^\circ=289-240(0.5)=169$. Therefore $c=13$, choice A. Choice B ($17$) is $\sqrt{8^2+15^2}$, which treats the angle as $90^\circ$ and ignores the $-2ab\cos C$ term. Choice C ($23$) adds the two sides, which would be the largest possible length only for a degenerate triangle. Choice D ($7$) subtracts them, the smallest possible length. A third side must lie strictly between $7$ and $23$, and the angle determines where.