Question

A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the the bottom of the first house is $30^{^\circ }$ . If the distance between the two houses is $6$ $\text{m}$ then the height of the first house is (in $m$ )

• A. $8 \sqrt{3}$
• B. $16 \sqrt{3}$
• C. $3 \sqrt{3}$
• D. $12 \sqrt{3}$

Answer 1

Answer: (A)

Let $\textit{D}$ be the position of window of second house and $\textit{BC}$ be the position of the first house.

In $\text{Δ}\textit{ADB}$ , $\textit{AD}=2\sqrt{3}$
$\textit{BD}=4\sqrt{3}$
In $\text{Δ}\textit{BCD}$ ,
$\text{cos}60^{^\circ }=\frac{\textit{BD}}{\textit{h}}$
$\therefore \textit{h}=8\sqrt{3}$