question_answer

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of \[{{60}^{o}}\] at the foot of the tower and the angle of elevation of the top of the tower from A or B is \[{{30}^{o}}\]. The height of tower is

A)  \[\frac{2a}{\sqrt{3}}\]                                      

B)  \[2a\sqrt{3}\]

C)  \[\frac{a}{\sqrt{3}}\]                            

D)  \[\sqrt{3}\]

Correct Answer: C

Solution :

            \[\Delta OAB\] is equilateral\[\Rightarrow \,r=a\] \[\therefore \,\,\ln \,\Delta OAC\,\] \[\frac{h}{a}=\tan {{30}^{0}}\]\[\Rightarrow \,h=\frac{a}{\sqrt{3}}\]