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The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of $100 m$ from its base is $45 ° .$ If the angle of elevation of the top of the pillar after completion at the same point is $60 °,$ then the height to be increased for the completion of the pillar in metres is

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$50 \sqrt{3}$

$100 \sqrt{2}$

$100 \sqrt{3}$

$100 (\sqrt{3} - 1)$

answer is D.

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Detailed Solution

$\begin{array}{l} P Q = O Q - O P = 100 \tan 60^{\circ} - 100 \tan 45^{\circ} \\ = 100 (\sqrt{3} - 1) \end{array}$

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