Question

There is flag-staff at the top of $10$ metres high tower. lf the flag-staff makes an angle ${\tan }^{-1}\left(1/8\right)$ at a point $24$ metres away from the tower, then the height of the flag staff in metres is

• A. $26/7$
• B. $27/8$
• C. $27/6$
• D. $26/3$

Answer 1

Answer: (A)

$26/7$

$tan\theta =\frac{1}{8},tan\alpha =\frac{10}{24}$
$=\frac{5}{12}$
$tan(\alpha +\theta )=\frac{h+10}{24}$
$\frac{tan\alpha +tan\theta }{1-tan\alpha tan\theta }=\frac{h+10}{24}$
$\frac{1}{8}+\frac{5}{12}1-\frac{5}{12}\times \frac{1}{8}=\frac{h+10}{24}$
$\frac{12+40}{(69-5)}=\frac{h+10}{24}$
$\frac{25\times 24}{91}=4+10$
$h=\frac{338}{91}=\frac{26}{7}$