[ Mutual relations between sides and angles of triangles (other).]

In triangle $ABC$, the height $AH$ is equal to the median $BM$. Find the angle $MBC$.

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Drop a perpendicular $M D$ from point $M$ to line $B C$. Then $M D=A H / 2=B M / 2$. In the right triangle $B D M$, the leg $M D$ is equal to half of the hypotenuse $B M$. Therefore, $\angle M B C=\angle M B D=30^{\circ}$.

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