Question

A flag staff on the top of the tower $80meter$ high, subtends an angle ${\tan }^{-1}\left(\frac{1}{9}\right)$ at point on the ground $100meters$ away from the foot of the tower. Find the height of the flag-staff.

• A. $20m$
• B. $30m$
• C. $25m$
• D. $35m$

Answer 1

Answer: (A)

$20m$

$\to$ Let, height of the flag stuff be $x$.

$\to$ Angle subtended by the tower.

$\therefore \theta ={\tan }^{-1}\left(\frac{80}{100}\right)=38.7$ degree.

$\to$ Angle subtended by the flag stuff

$\therefore {\tan }^{-1}\left(7/9\right)=6.3$ degree.

$\to$ total angle subtended $=38.7+6.3$

$=45$ degree.

$\to$ As shown in triangle

$\tan 45=\frac{x+80}{100}$

$\therefore 1=\frac{x+80}{100}$

$\therefore x=100-80$

$\therefore x=20$