25. Exemplar example problems III

The angle of elevation of a cloud from a point \(h\) metres above the surface of a lake is \(\theta\) and the angle of depression of its reflection in the lake is \(\phi\). Prove that the height of the cloud above the lake is \(h \left(\frac{tan \ \phi + tan \ \theta}{tan \ \phi - tan \ \theta} \right)\).