$(50$ points$)$ The cast iron block with cross$-$sectional dimensions of $75$ mm by $75$ mm consists of two pieces. The pieces are prevented from sliding along the $55$ inclined joint by the steel key, which is $75-mm-$long. Determine the smallest safe dimensions $b$ and $h$ of the key if the working stresses are $240$ MPa for cast iron in bearing and $300$ MPa for the key in shear.