An engineer standing at a point $P$ wishes to determine the width of a new rectangular pond. She finds the distance to the western-most point $A$ of the pond from $P$ to be $60$ m, while the distance to the northern-most point $B$ of the pond from $P$ is $80$ m. If the angle between the two lines of sight at $P$ is $60^\circ$, then the width $AB$ in metres of the pond is, where $AB$ is not parallel to line of North-South: