40. Exemplar exercise problems XV

A window of a house is \(h \ \text{metres}\) above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be \(\alpha\) and \(\beta\), respectively. Prove that the height of the other house is \(h(1 + tan \ \alpha \ cot \ \beta)\) \(\text{metres}\).