Answer. $\angle B=90^{\circ}, \angle C=60^{\circ}$.

Solution. Given that $\angle A=30^{\circ}$, the height drawn from vertex $C$ is half of $A C$, therefore, the median drawn from vertex $B$ is also half of $A C$. It follows that vertex $B$ lies on the circle with diameter $A C$, hence $\angle B=90^{\circ}, \angle C=90^{\circ}-30^{\circ}=60^{\circ}$.
10.2. In triangle $A B C$, the measure of angle $A$ is 30 degrees, and the length of the median drawn from vertex $B$ is equal to the length of the altitude drawn from vertex $C$. Find the measures of angles $B$ and $C$.