Height of a mast from two angles of elevation and a walk on a bearing, using the cosine rule

A vertical mast \(PQ\) stands with its foot \(P\) on horizontal ground. The point \(R\) on the ground is due south of \(P\), and the angle of elevation of \(Q\) from \(R\) is \(35^\circ\). A surveyor walks \(40\text{ m}\) from \(R\) on a bearing of \(060^\circ\) to the point \(S\), from which the angle of elevation of \(Q\) is \(25^\circ\). The diagram below is not drawn to scale.

Find the height of the mast, correct to 3 significant figures.[7]