jmc

Because $△VWX$ is a right triangle, $\tan V=\frac{WX}{VW}$.

By the Pythagorean Theorem, $$WX=\sqrt{V{X}^2-W{X}^2}=\sqrt{13-9}=\sqrt{4}=2.$$Then $\tan V=\boxed{\frac{2}{3}}$.