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From the top of a tower of height $60$ m, the angles of depression of the top and the bottom of a building are observed to be $30 °$ and $60 °$ respectively. Find the height of the building.

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20

60

80

40

answer is D.

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Detailed Solution

It is given that the angles of depression of the top and the bottom of a building are observed to be

30 °

and

60 °

from the top of a tower of height

60

m.
According to the given data the figure has been drawn below.
Let

BD = CE = h,

AB = 60 - h,

BC = ED

Distance between tower and building be

BC = ED = x .

ΔAED,

tan θ = P e r p e n d i c u l a r b a s e

\tan 60 ° = \frac{AD}{ED}

= \frac{60}{x}

\Rightarrow \sqrt{3} = \frac{60}{x}

∵ tan 60 ° = 3

\Rightarrow x = 20 \sqrt{3} m

ΔABC,

tan θ = P e r p e n d i c u l a r b a s e

\tan 30 ° = \frac{AB}{BC}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{60 - h}{20 \sqrt{3}}

∵ tan 30 ° = 13

\Rightarrow h = 40 m

So, the height of the building is

40 m

.
So the correct option is 4.

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