From the top of a tower $100\ \text{m}$ high a man observes the angles of depression of two ships $A$ and $B$, 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 $B$ to the nearest metre. (Use Mathematical Tables for this question.)