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A house subtends a right angle at the window of the opposite house and the angle of elevation of the window from the bottom of the first house is $60^{o}$ . If the distance between the two houses is 6 m, then the height of the first house is?

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6 \sqrt{3} m

8 \sqrt{3} m

4 \sqrt{3} m

None of these

answer is B.

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Detailed Solution

It is given that the angle of elevation of the window from the bottom of the first house is

60^{o}

The distance between the two houses be 6 m.
We have to find the height of the first house
We use

tanθ = \frac{Opposite Side}{Adjacent Side}

∆ ADC,

\frac{AD}{AB} = \tan 60 °

\Rightarrow \frac{6 \sqrt{3}}{AB} = \sqrt{3}

\Rightarrow AB = 6

\Rightarrow DC = 6

m [since AB=DC]
Similarly, in

∆ DEC,

\frac{DC}{EC} = \tan 60 °

\Rightarrow \frac{6}{EC} = \sqrt{3}

[since

\tan 60 ° = \sqrt{3}

]

\Rightarrow EC = 2 \sqrt 3

\Rightarrow h = EC + CB

\Rightarrow h = 2 \sqrt{3} + 6 \sqrt{3}

\Rightarrow h = 8 \sqrt 3 m

Hence, the height of the first house is 8

\sqrt{3} m .

Therefore, the correct option is 2.

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