Navigational Trigonometry: Analyzing Bearings and Positions of Three Reservoirs

In the diagram, \(P\), \(Q\) and \(R\) represent three reservoirs.

\(P\) is \(22\) km from \(Q\) on a bearing of \(140{}^\circ\) and \(R\) is \(20\) km from \(P\) on a bearing of \(290{}^\circ\).

1. Calculate the bearing of \(Q\) from \(P\).
2. A cyclist leaves \(P\) and cycled along \(PQ\) towards \(Q\) at a steady speed of \(10\) km/h.
   He stops at a point \(S\) which is due east of \(R\).
   1. Mark the point \(S\) on the diagram.
   2. Calculate the distance \(PS\).
   3. Calculate the time taken to reach \(S\) from \(P\), giving your answer in minutes.
3. A tower of height \(60\) m is located at \(P\).
   What is the angle of elevation of the top of the tower from the cyclist at point \(S\)?