The figure below shows a flying kite. At a certain moment, the kite string forms an angle of elevation of \(75^\circ\) from point \(A\) on the ground. At the same moment, the angle of elevation of the kite at point \(B\), \(240\) ft from \(A\) on level ground, is \(45^\circ\). What is the length, in feet, of the string?