A road runs from \(A\) due East to \(B\), \(500\) yd. distant. The bearings of a tree from \(A\) and \(B\) are \(048^\circ\) and \(296^\circ\) respectively. Find the distance, correct to the nearest yard, of the tree from the road.

A road runs from \(A\) due East to \(B\), \(500\) yd. distant. The bearings of a tree from \(A\) and \(B\) are \(048^\circ\) and \(296^\circ\) respectively. Find the distance, correct to the nearest yard, of the tree from the road.