An aeroplane $P$ is moving in the air along a straight line path which passes through the points $P_1$ and $P_2$, and makes an angle $\alpha$ with the ground. Let $O$ be the position of an observer. When the plane is at the position $P_1$ its angle of elevation is $30^\circ$ and when it is at $P_2$ its angle of elevation is $60^\circ$ from the position of the observer. Moreover, the distances of the observer from the points $P_1$ and $P_2$ respectively are 100 metres and $500/3$ metres. Then $\alpha$ is equal to (a) $\tan^{-1}\{(2-\sqrt{3})/(2\sqrt{3}-1)\}$ (b) $\tan^{-1}\{(2\sqrt{3}-3)/(4-2\sqrt{3})\}$ (c) $\tan^{-1}\{(2\sqrt{3}-2)/(5-\sqrt{3})\}$ (d) $\tan^{-1}\{(6-\sqrt{3})/(6\sqrt{3}-1)\}$
(d) $\tan^{-1}\{(6-\sqrt{3})/(6\sqrt{3}-1)\}$
An aeroplane $P$ is moving in the air along a straight line path which passes through the points $P_1$ and $P_2$, and makes an angle $\alpha$ with the ground. Let $O$ be the position of an observer. When the plane is at the position $P_1$ its angle of elevation is $30^\circ$ and when it is at $P_2$ its angle of elevation is $60^\circ$ from the position of the observer. Moreover, the distances of the observer from the points $P_1$ and $P_2$ respectively are 100 metres and $500/3$ metres.
Then $\alpha$ is equal to\\
(a) $\tan^{-1}\{(2-\sqrt{3})/(2\sqrt{3}-1)\}$\\
(b) $\tan^{-1}\{(2\sqrt{3}-3)/(4-2\sqrt{3})\}$\\
(c) $\tan^{-1}\{(2\sqrt{3}-2)/(5-\sqrt{3})\}$\\
(d) $\tan^{-1}\{(6-\sqrt{3})/(6\sqrt{3}-1)\}$