Question

A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is $60°$. If the distance between the two houses is $6$meter, then the height of the first house is

• A. $8\sqrt{3}$
• B. $6\sqrt{3}$
• C. $4\sqrt{3}$
• D. None of these

Answer 1

The correct option is A

$8\sqrt{3}$

Step1. Draw the diagram :

Step2. Find the height of the first house $AB$:

From the figure, $\angle DBC=60°,\angle ADB=90°,\angle EDB=\angle DBC=60°$

$\angle ADB=\angle ADE+\angle EDB=90°$

$\angle ADE=90°–60°=30°$

In $△AED$

We have

$\tan 30°=\frac{AE}{ED}$

$\Rightarrow$ $\frac{1}{\sqrt{3}}=\frac{AE}{6}$

$\Rightarrow$ $AE=\frac{6}{\sqrt{3}}$

$\Rightarrow$ $AE=2\sqrt{3}$ meter

$\tan 60°=\frac{EB}{6}$

$\Rightarrow$ $\sqrt{3}=\frac{EB}{6}$

$\Rightarrow$ $EB=6\sqrt{3}$meter

So, the height of the first house $AB$

$$\begin{gathered} =AE+EB \\ =2\sqrt{3}+6\sqrt{3} \end{gathered}$$

$=8\sqrt{3}$meter

Hence, the correct option is (A).