question_answer

At a distance 2h from the foot of a tower of height h, the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

A) \[\frac{5h}{3}\]

B) \[\frac{4h}{3}\]

C) \[\frac{7h}{5}\]

D) \[\frac{3h}{2}\]

Correct Answer: A

Solution :

\[\tan \alpha =\frac{1}{2}\] and \[BC=a\text{ }km\] \[\tan 2\alpha =\frac{2\tan \alpha }{1-{{\tan }^{2}}\alpha }\Rightarrow \frac{p+h}{2h}=\frac{1}{1-\frac{1}{4}}\] \[\Rightarrow \] \[\frac{p+h}{2h}=\frac{4}{3}\Rightarrow p=\frac{5h}{3}\].