14. Five mark exercise problems VI

1. If the angle of elevation of a cloud from a point '\(h\)' meters above a lake is \(\theta_1\) and the angle of depression of its reflection in the lake is \(\theta_2\). Prove that the height that the cloud is located from the lake is \(\frac{h(tan \ \theta_1 + tan \ \theta_2)}{tan \ \theta_2 - tan \ \theta_1}\).

 

2. From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be \(30^{\circ}\) and \(60^{\circ}\). If the height of the lighthouse is \(h\) meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is \(\frac{4h}{\sqrt{3}} \ m\).