Height of a mast from a sloping triangle solved by the sine rule and one angle of elevation

A vertical mast \(FT\) has its foot \(F\) on horizontal ground. The points \(G\) and \(H\) lie on the ground, with \(GH=60\text{ m}\). In triangle \(TGH\), \(\angle TGH=70^\circ\) and \(\angle GHT=50^\circ\). The angle of elevation of \(T\) from \(G\) is \(38^\circ\). The diagram below is not drawn to scale.

Find the height of the mast, correct to 3 significant figures.[6]