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Apoorv is standing in the centre of a rectangular
park and observes that the angle of elevation of the
top of a lamp post at a corner of the park in 60°. He then
moves diagonally towards the opposite corner of the park
and observes that the angle of elevation is now $β$ then the
value of $β$ is

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45°

30°

$\tan^{- 1} (\sqrt{3} / 2)$

$\tan^{- 1} (2 / \sqrt{3})$

answer is C.

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Detailed Solution

Let P and $Q$ be the opposite corners of the
park with centre $O$ . If h is the height of the lampost at $P$

then $O P = h \cot 60^{\circ} = h / \sqrt{3} .$

$\begin{array}{l} P Q = h \cot β = 2 O P = 2 h / \sqrt{3} \\ \Rightarrow \cot β = (2 / \sqrt{3}) \Rightarrow β = \tan^{- 1} (\sqrt{3} / 2) \end{array}$

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