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Q.

If two towers of height h₁ and h₂ 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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a

$1 : 3$

b

$1 : \sqrt{3}$

c

$3 : 1$

d

$\sqrt{3} : 1$

answer is A.

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Detailed Solution

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$\tan 60 ° = \frac{h_{1}}{a} \sqrt{3} = \frac{h_{1}}{a} h_{1} = \sqrt{3} a \to (1) \tan 30 ° = \frac{h_{2}}{a} \frac{1}{\sqrt{3}} = \frac{h_{2}}{a} h_{2} = \frac{a}{\sqrt{3}} \to (2) h_{1} : h_{2} = \sqrt{3} a : \frac{a}{\sqrt{3}} = \sqrt{3} a \times \frac{\sqrt{3}}{a} ∴ h_{1} : h_{2} = 3 : 1$

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If two towers of height h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1:h2 is