Question

The angle of elevation of a cloud from a point 60 m above a lake is 30^o and the angle of depression of the reflection of cloud in the lake is 60^o. Find the height of the cloud.

Answer 1

$$\begin{gathered} \mathrm{Let}: \\ BC=h\mathrm{m} \\ \mathrm{And}, \\ AB=b\mathrm{m} \\ \mathrm{In}△ACB, \\ \tan 30°=\frac{h}{b} \\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{b} \\ \Rightarrow b=\sqrt{3}h...\left(\mathrm{i}\right) \\ \mathrm{In}△ABD, \\ \tan 60°=\frac{60+60+h}{b} \\ \Rightarrow \sqrt{3}=\frac{120+h}{b} \\ \Rightarrow b=\frac{120+h}{\sqrt{3}}...\left(\mathrm{ii}\right) \\ \mathrm{From}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ \sqrt{3}h=\frac{120+h}{\sqrt{3}} \\ \Rightarrow 3h=120+h \\ \Rightarrow 120=2h \\ \Rightarrow 60=h \\ \therefore \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cloud}=60+h=60+60=120\mathrm{m} \end{gathered}$$