Height of a tower from two angles of elevation measured on a straight line away from its base

A vertical radio mast \(FT\) stands on horizontal ground, with its foot at \(F\) and its top at \(T\). The height of the mast is \(h\) metres.

A surveyor stands at the point \(P\), where \(PF=x\) metres, and measures the angle of elevation of \(T\) as \(52^\circ\). She then walks \(45\) metres directly away from the mast to the point \(Q\), where the angle of elevation of \(T\) is \(24^\circ\). The points \(Q\), \(P\) and \(F\) lie on a straight line.

1. Express each of the following in terms of \(h\) and \(x\).[2]
   1. \(\tan52^\circ\)
   2. \(\tan24^\circ\)
2. Hence find \(x\).[2]
3. Find \(h\).[2]