35. Exemplar exercise problems X

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height \(h\). At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are \(\alpha\) and \(\beta\), respectively. Prove that the height of the tower is \(\left(\frac{h \ tan \ \alpha}{tan \ \beta - tan \ \alpha} \right)\).