Question

A flag-staff of 5m high stands on a building of 25 m high. At an observer at a 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. $\frac { 5 \sqrt { 3 } } { 2 }$
• B.
• C.
• D. None of these

Answer 1

Answer: (B)

Answer 2

We have, $\tan \alpha = \frac { 5 } { x }$ and $\tan 2 \alpha = \frac { 30 } { x }$

$\therefore$ $\tan 2 \alpha = \frac { 30 } { 5 \cot \alpha }$ ⇒$\tan 2 \alpha = 6 \tan \alpha$

⇒ $3 - 3 \tan ^ { 2 } \alpha = 1$ ⇒$\tan \alpha = \sqrt { \frac { 2 } { 3 } }$

$x = 5 \cot \alpha = 5 \sqrt { \frac { 3 } { 2 } }$