Question

A flag-staff $20$ metres long standing on a wall $10$ metres high subtends an angle whose tangent is $0.5$ at a point on the ground. lf $\theta$ is the angle subtended by wall at that point then $\tan \theta =$

• A. $1$
• B. $\frac{1}{3}$
• C. $1$ or $\frac{1}{3}$
• D. $2$

Answer 1

The correct option is C $1$ or $\frac{1}{3}$

$tan\alpha =\frac{1}{2}$
$tan(\alpha +\theta )=\frac{30}{d}$
$tan\theta =\frac{10}{d}$
$\frac{(tan\alpha +tan\theta )}{1-tan\alpha tan\theta }=3tan\theta$
$\frac{1+2tan\theta }{2-tan\theta }=3tan\theta$
$1+2tan\theta =6tan\theta -3tan\theta$
$3tan\theta -4tan\theta +1=0$
$tan\theta =1,\frac{1}{3}$