Two lamp posts $\mathit{A}\mathit{B}$ and $\mathit{C}\mathit{D}$ each of height $100\mathrm{m}$ are on either side of the road. $\mathit{P}$ is a point on the road between the two lamp posts. The angles of elevation of the top of the lamp posts from the point $\mathit{P}$ are ${60}^{\circ }$ and ${40}^{\circ }$. Find the distances $\mathit{P}\mathit{B}$ and $\mathit{P}\mathit{D}$.