From the top of a tower $100\mathrm{m}$ high a man observes the angles of depression of two ships $\mathit{A}$ and $\mathit{B}$, on opposite sides of the tower as ${45}^{\circ }$ and ${38}^{\circ }$ respectively. If the foot of the tower and the ships are in the same horizontal line find the distance between the two ships A and $\mathit{B}$ to the nearest metre.
(Use Mathematical Tables for this question.)