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Q.

The angle of elevation of top of a pole from two points A and B on the horizontal line lying on either side of the pole are observed to be 30° and 60°. If $A B = 100 m$ then height of the pole is

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a

$10 \sqrt{3} m$

b

$20 \sqrt{3} m$

c

$15 \sqrt{3} m$

d

$25 \sqrt{3} m$

answer is D.

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Detailed Solution

Question Image

Let $A C = x$

Then $B C = 100 - x$

From $Δ A D C$

$\tan 30 ° = \frac{h}{x} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{x} \Rightarrow x = \sqrt{3} h$

$\begin{array}{l} I n Δ B C D, \tan 60 ° = \frac{h}{100 - x} \\ \Rightarrow (100 - x) \sqrt{3} = h \\ \Rightarrow h = 100 \sqrt{3} - h (\sqrt{3}) (\sqrt{3}) \\ \Rightarrow h = 100 \sqrt{3} - 3 h \\ \Rightarrow 4 h = 100 \sqrt{3} \\ ∴ h = 25 \sqrt{3} m \end{array}$

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