Use the cosine law to find the length of a:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ a=\sqrt[]{b^2+c^2-2bc\cos A} \end{gathered}[/tex][tex]\begin{gathered} a=\sqrt[]{10^2+13^2-2(10)(13)\cos 33} \\ \\ a=\sqrt[]{100+169-260\cos 33} \\ \\ a=\sqrt[]{269-260\cos 33} \\ \\ a=\sqrt[]{50.94565233} \\ \\ a\approx7.13762 \end{gathered}[/tex]
Having the value of a, use sine law to find the measure of angle B:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} b\cdot\frac{\sin A}{a}=\sin B \\ \\ B=\sin ^{-1}(b\cdot\frac{\sin A}{a}) \\ \\ B=\sin ^{-1}(10\cdot\frac{\sin 33}{7.13762}) \\ \\ B=49.734 \end{gathered}[/tex]Then, the measure of angle B is 49.734º
