Two men standing on same side of a pillar $75$ meter high, observe the angles of elevation of the top pillar to be $30^o$ and $60^o$ respectively the distance between two men is:

The angle elevation of the top $Q$ of a vertical tower $PQ$ from a point $X$ on the ground is $60$ degree.From a point $Y$,$40$m vertically above $X$,the angles of elevation of the top $Q$ of the tower is ${45}^{\circ }$.Find the height of the tower $PQ$ and the distance $PX.$(Use $\sqrt{3}=1.732$)