Question

A flag staff 5 mt. high stands on a building $25mt$. high.An observer is at the height of $30m$. The flag staff and the building subtend equal angles. The distance of the observer from the top of the flag staff is

• A. $\frac{5\sqrt{3}}{\sqrt{8}}$
• B. $\frac{5\sqrt{3}}{\sqrt{2}}$
• C. $\frac{4\sqrt{3}}{\sqrt{2}}$
• D. $\frac{7\sqrt{3}}{\sqrt{2}}$

Answer 1

The correct option is B $\frac{5\sqrt{3}}{\sqrt{2}}$

In $△DBC$

$\tan \alpha =\frac{5}{x}.......\left(i\right)$

and In $△DAC$

$\tan 2\alpha =\frac{30}{x}$

$\Rightarrow \frac{2\tan \alpha }{1-{\tan }^2\alpha }=\frac{30}{x}$

$\Rightarrow \frac{2\frac{5}{x}}{1-\frac{25}{x^2}}=\frac{30}{x}$

$\Rightarrow \frac{10x}{x^2-25}=\frac{30}{x}$

$\Rightarrow 10x^2=30x^2-750$

$\Rightarrow 20x^2=750$

$\Rightarrow x^2=\frac{75}{2}$

$\Rightarrow x=5\frac{\sqrt{3}}{\sqrt{2}}m$