Question

Flagstaff on the top of a tower $80$ metres high subtends angle ${\tan }^{-1}\frac{1}{9}$ at a point on the ground $100$ metres from the foot of the tower. The height of the Flagstaff (in metres) is

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

The correct option is B $20$

From the figure

BC= tower, AB=flag-staff
$\tan \beta =\frac{4}{5}$, $\tan \alpha =\frac{1}{9}$
$\tan (\alpha +\beta )=\frac{80+h}{100}$
$\Rightarrow \frac{\frac{4}{5}+\frac{1}{9}}{1-\frac{4}{45}}=\frac{80+h}{100}$.....using $tan(A+B)=\frac{tanA+tanB}{1-tanA.tanB}$
$\Rightarrow \frac{80+h}{100}=1$
$\Rightarrow h=20m$