University Calculus: Early Transcendentals (3rd Edition)

The length of side $c$ is $\sqrt7$.
$$a = 2 \hspace{1cm}b=3\hspace{1cm}C=60^\circ$$ - Recall the law of cosines: $$c^2=a^2+b^2-2ab\cos C$$ Therefore, we can calculate the length of side $c$: $$c^2=2^2+3^2-2\times2\times3\times\cos60^\circ$$ $$c^2=4+9-12\times\frac{1}{2}$$ $$c^2=13-6=7$$ $$c=\sqrt7$$ (because the length of a side of a triangle is positive)