question_answer

The angle of elevation of the top of a tower from the top of a house is\[{{60}^{o}}\]and the angle of depression of its base is\[{{30}^{o}}\]. If the horizontal distance between the house and the tower be 12 m, then the height of the tower is

A) \[48\,\sqrt{3}\,\,m\]

B) \[16\,\sqrt{3}\,\,m\]

C) \[24\,\sqrt{3}\,\,m\]

D) \[16/\,\sqrt{3}\,\,m\]

Correct Answer: B

Solution :

\[h=12\tan {{30}^{o}}=\frac{12}{\sqrt{3}}\] and \[H=12\tan {{60}^{o}}+\frac{12}{\sqrt{3}}\]           = \[12\sqrt{3}+\frac{12}{\sqrt{3}}=16\sqrt{3}m\].