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 $30^{\circ}$ . What is the height of the tower?

$12 m$

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$14 m$

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$10 m$

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$15 m$

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Solution

The correct option is A
$12 m$

$S R = P Q = 2 m$
$P S = Q R = 10 \sqrt{3} m$
$tan 30^{\circ} = \frac{T S}{P S}$
$\frac{1}{\sqrt{3}} = \frac{T S}{10 \sqrt{3}}$
$T S = \frac{10 \sqrt{3}}{\sqrt 3} = 10 m$
$T R = T S + S R = 10 + 2 = 12 m$

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