Question

A flagstaff on the top of a tower $80m$ high, subtends an angle ${\tan }^{-1}\left(\frac{1}{9}\right)$ at point on the ground $100m$ from the foot of the tower. The height of the flagstaff is

• A. $40m$
• B. $30m$
• C. $20m$
• D. $\frac{100}{\sqrt{2}}m$

Answer 1

Answer: (C)

$20m$

R.E.F image

Given,

$BC=80m$

Let $AB=x$

$\alpha =ta{n}^{-1}\frac{1}{4}$

$=1tan\alpha =\frac{1}{4}$

$tan\beta =\frac{BC}{CD}=\frac{80}{100}=\frac{4}{5}$

$tan(\alpha +\beta )=\frac{AB+80}{100}$

$\frac{\frac{1}{9}+\frac{4}{5}}{1-\frac{1}{9}\times \frac{4}{5}}=\frac{AB+80}{100}$

$\therefore AB=20m$

$\therefore$ Height of the flagstaff is 20 m