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An observer $2 m$ tall is $10 \sqrt{3} m$ away from a tower. The angle of elevation from his eye to the top of the tower is $30 °$ . The height of the tower is

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$12 m$

$5 m$

$15 m$

$2 m$

answer is A.

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Detailed Solution

$S R = P Q = 2 m$

$P S = Q R = 10 \sqrt{3} m$

In $Δ P S T$ , $\tan 30 ° = \frac{T S}{P S}$

$\Rightarrow \frac{1}{\sqrt{3}} = \frac{T S}{10 \sqrt{3}}$

$∴ T S = 10 m$

$∴$ The height of the tower is $h = T S + S R$

$h = 10 + 2$

$h = 12 m$

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