There is a small island in the middle of a $100 \mathrm{m}$ wide river and a tall tree stands on the island. $\mathrm{P}$ and $\mathrm{Q}$ are points directly opposite each other on the two banks, and in line with the tree. If the angles of elevation of the top of the tree from $\mathrm{P}$ and $\mathrm{Q}$ are respectively $30°$ and $45°,$ find the height of the tree.