question_answer

The angles of elevation of the top of a tower from two points distant a and b (a > b) from its foot and in the same straight line from it are \[30{}^\circ \] and \[60{}^\circ \]. The height of the tower is

A) \[\frac{a}{b}\]

B) \[\sqrt{\frac{a}{b}}\]

C) \[ab\]

D) \[\sqrt{ab}\]

Correct Answer: D

Solution :

 From \[\Delta \,\,AOT,\] \[h=a\,\,\tan \,{{30}^{o}}\] From \[\Delta \,BOT,\]  \[h=b\,\tan {{60}^{o}}\] \[\therefore \]  \[{{h}^{2}}=ab\,\,\tan {{30}^{o}}\tan {{60}^{o}}\]                 \[=ab\,\frac{1}{\sqrt{3}}.\sqrt{3}\] or            \[h=\sqrt{ab}\]