Question

The flag staff of height $10$ metres is placed on the top of a tower of height $30$ metres. At the top of a tower of height $40$ metres, the flag staff and the tower subtend equal angles then the distance between the two towers (in metres) is

• A. $10\sqrt{2}$
• B. $20\sqrt{2}$
• C. $30\sqrt{2}$
• D. $40\sqrt{2}$

Answer 1

The correct option is A $10\sqrt{2}$

$\tan 2\theta =\frac{40}{d}$ ...(i)
$\Rightarrow \frac{2\tan \theta }{1-{\tan }^2\theta }=\frac{40}{d}$

$\tan \theta =\frac{10}{d}$ ...(ii)

Substituting (ii) in (i), we get

$\frac{2\frac{10}{d}}{1-\frac{(10{)}^2}{d^2}}=\frac{40}{d}$

$\Rightarrow \frac{d}{d^2-{10}^2}=\frac{2}{d}$

$\Rightarrow d^2=2d^2-2\times {10}^2$
$\Rightarrow d^2=2\times {10}^2$
$\Rightarrow d=10\sqrt{2}m$