The horizontal distance between two towers is 30 metres, from the foot of the first tower the angle of elevation of the top of the second tower is $60 °$ .From the top of the second tower the angle of depression of the top of the first tower is $30 °$ . The height of the smaller tower is

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$20 (\sqrt{3} + 1) m t s$

$20 (\sqrt{3} - 1) m t s$

$20 \sqrt{3} m t s$

20mts

answer is C.

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Detailed Solution

In $Δ A E C, \tan 30 ° = \frac{h}{30}$

$\Rightarrow h = \frac{30}{\sqrt{3}} = 10 \sqrt{3} m$

in $Δ A B D, \tan 60 ° = \frac{h + x}{30}$

$\begin{array}{l} \Rightarrow h + x = 30 \sqrt{3} \\ \Rightarrow 10 \sqrt{3} + x = 30 \sqrt{3} \\ \Rightarrow x = 20 \sqrt{3} m \end{array}$

$∴$ Height of the small towel $(x) = 20 \sqrt{3} m$

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