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

• Correct answer
  A

  $8 \sqrt{3} \mathrm{~m}$
• B

  $6 \sqrt{3} \mathrm{~m}$
• C

  $4 \sqrt{3} \mathrm{~m}$
• D

  None of these

Solution

Let $P Q$ be the house subtending a right angle at the window $B$ of opposite house $A B$
In $\triangle P A B$, we have $\tan 60^{\circ}=\frac{A B}{6}=A B=6 \sqrt{3} \mathrm{~m}$ In $\triangle C B Q$, we have $\tan 30^{\circ}=\frac{h-C P}{B C}$ $\begin{array}{ll}\Rightarrow & \frac{1}{\sqrt{3}}=\frac{h-6 \sqrt{3}}{6} \quad[\because A B=C P, B C=A P] \\ \Rightarrow & h=6\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right) \\ \Rightarrow & h=8 \sqrt{3} \mathrm{~m}\end{array}$

Hence, the correct answer is option: 'A'.