There is a small island in the middle of a $100\,\text{m}$ wide river and a tall tree stands on the island. $P$ and $Q$ are points directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of the tree from $P$ and $Q$ are respectively $30^{\circ}$ and $45^{\circ}$, find the height of the tree. (Use $\sqrt{3}=1.732$ )