Question

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 be 6 m, then the height of the first house is?

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

Answer 1

Answer: (B)

$8\sqrt{3}\text{m}$

In $△ADC$

$\frac{AD}{AB}=\tan {60}^{\circ }\frac{6\sqrt{3}}{AB}=\sqrt{3}\Rightarrow AB=6\Rightarrow DC=6$

In $△DEC$

$\frac{DC}{EC}=\tan {60}^{\circ }\frac{6}{EC}=\sqrt{3}\Rightarrow EC=2\sqrt{3}h=EC+CBh=2\sqrt{3}+6\sqrt{3}h=8\sqrt{3}$

So option $B$ is correct.