The angles of elevation of the top of from two points P and Q at distance m^2 and n^2 respectively, from the base and in the same straight line with it are complementary. The height of the tower is-

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& \text{tan }\theta =\frac{H}{m^2}\\ & \Rightarrow \tan \left(90^{\circ }-\theta \right)=\frac{H}{n^2}\\ & \Rightarrow \cot \theta =\frac{H}{n^2}\\ & \Rightarrow \tan \theta .\cot \theta =\frac{H}{m^2}\times \frac{H}{n^2}\\ & \Rightarrow \frac{H}{m^2}\times \frac{H}{n^2}=1\\ & \Rightarrow H^2=m^2{n}^2\\ & \Rightarrow H=mn\end{array}$$