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Q.

From the top of a ‘h’ meters high cliff the angle depression of the top and bottom of a tower are observed to be $30^{0}$ and $60^{0}$ respectively the height of the tower is

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a

$\frac{h}{4}$

b

$\frac{h}{2}$

c

$\frac{h}{3}$

d

$\frac{2 h}{3}$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

$\frac{h - x}{y} = \tan 30$

$y = (h - x) \times \sqrt{3}$

$\frac{h}{y} = \tan 60^{0} = h = \sqrt{3} y$

$y = \frac{1}{\sqrt{3}} h \Rightarrow x = \frac{2 h}{3}$

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