Question

The height of a house subtends a right angle at opposite window from the base of the house is ${60}^0$. If the width of the road be 6 metres, then the height of the house is

• A. $6\sqrt{3}m$
• B. $8\sqrt{3}m$
• C. $10\sqrt{3}m$
• D. $3\sqrt{6}$

Answer 1

Answer: (B)

$8\sqrt{3}m$

Given $\angle DBC={60}^0$ and $\angle ADB={90}^0$ from figure we know that $\angle EDB=\angle DBC={60}^0$

Since $\angle ADB=\angle ADE+\angle EDB={90}^0$

$\angle ADE={90}^0-{60}^0={30}^0$

From AED ,

$\tan 30=\frac{AE}{6}$

$AE-2\sqrt{3}m$

From EDC,

$\tan 60=\frac{EB}{6}$

$EB=6\sqrt{3}m$

Height of the house =$AE+EB=2\sqrt{3}+6\sqrt{3}=8\sqrt{3}m$