Question

A flagstaff $5$ m high stands on a building $25$ m high. As observed from a point at a height of $30$ m, the flagstaff and the building subtend equal angles. The distance of the observer from the top of the flagstaff is

• A. $\frac{5\sqrt{3}}{2}$
• B. $5\sqrt{\frac{3}{2}}$
• C. $5\sqrt{\frac{2}{3}}$
• D. None of thses

Answer 1

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

OB is the bisector of DOAC of DAOC
$\therefore \frac{OC}{OA}=\frac{BC}{AB}=\frac{x}{\sqrt{x^2+{30}^2}}=\frac{5}{25}$
$\Rightarrow x=\frac{30}{\sqrt{24}}=\frac{30}{2\sqrt{6}}$
$\therefore x=5\sqrt{\frac{3}{2}}$