A lower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is

Answer: Option C

Let CD is the tower and A is a point such that the angle of elevation of C is 30°
B is and their point h m high of A and angle of depression of D is 60°

$$\begin{array}{rl}& \text{The}AB=hm\\ & \text{Let}CD=Hm\text{and }AD=x\\ & \text{Now}\text{in}\text{right}\Delta ABD,\\ & \tan \theta =\frac{AB}{AD}\\ & \Rightarrow \tan 60^{\circ }=\frac{h}{x}\\ & \Rightarrow \sqrt{3}=\frac{h}{x}\\ & \Rightarrow x=\frac{h}{\sqrt{3}}.......(\text{i})\\ & \text{Similarly in right }\Delta ACB,\\ & \tan 30^{\circ }=\frac{CD}{AD}\\ & \Rightarrow \frac{1}{\sqrt{3}}=\frac{H}{x}\\ & \Rightarrow x=\sqrt{3}H.......\left(\text{ii}\right)\\ & \text{From}\left(\text{i}\right)\text{and}\left(\text{ii}\right)\\ & \sqrt{3}H=\frac{h}{\sqrt{3}}\\ & H=\frac{h}{\sqrt{3}\times \sqrt{3}}=\frac{h}{3}\\ & \therefore \text{Height of tower}=\frac{h}{3}\end{array}$$