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If two towers of height $h_{1}$ and $h_{2}$ subtend angles of $60 °$ and $30 °$ respectively at the mid-point of the line joining their feet, then $h_{1} : h_{2}$ is

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3 : 1

1 : 3

\sqrt{3} : 1

1 : \sqrt{3}

answer is A.

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Detailed Solution

$\tan 60 ° = \frac{h_{1}}{a}$

$\sqrt{3} = \frac{h_{1}}{a}$

$h_{1} = \sqrt{3} a$ $\to (1)$

$\tan 30 ° = \frac{h_{2}}{a}$

$\frac{1}{\sqrt{3}} = \frac{h_{2}}{a}$

$h_{2} = \frac{a}{\sqrt{3}} \to (2)$

$h_{1} : h_{2} = \sqrt{3} a : \frac{a}{\sqrt{3}}$

$= \sqrt{3} a \times \frac{\sqrt{3}}{a}$

$= 3$

$∴ h_{1} : h_{2} = 3 : 1$

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