Angles of elevation of the top of a mast from two points on a straight path and the mast's height

A vertical radio mast of height \(h\) metres stands on level ground. A hiker walks along a straight horizontal path directly towards the foot of the mast.

From the point \(P\), the angle of elevation of the top of the mast is \(22^\circ\). The hiker walks \(85\) metres further to the point \(Q\), where the angle of elevation of the top of the mast is \(51^\circ\). The foot of the mast is \(F\), and \(QF=x\) metres.

1. Find, in terms of \(h\) and \(x\), an expression for
   1. \(\tan51^\circ\);
   2. \(\tan22^\circ\).[2]
2. Hence find \(x\).[2]
3. Find \(h\).[2]