Question

A statue standing on the top of a pillar $25m$ heigh subtends an angle whose tangent is $0.125$ at a point $60m$ from the foot of the pillar the best approximation for the height of the statue is

• A. $9.27m$
• B. $9.28m$
• C. $9.29m$
• D. $9.30m$

Answer 1

The correct option is C $9.29m$

Given

$\tan \theta =0.125=\frac{1}{8}$

$\tan \alpha =\frac{25}{60}=\frac{5}{12}$ [$\because$ from the figure]

According to question,

$\tan (\alpha +\theta )=\frac{25+h}{60}$

$\Rightarrow \frac{\tan \alpha +\tan \theta }{1-\tan \alpha .\tan \theta }=\frac{25+h}{60}$

$\Rightarrow \frac{\frac{5}{12}+\frac{1}{8}}{1-\frac{5}{12}.\frac{1}{8}}=\frac{25+h}{60}$

$\Rightarrow \frac{10+3}{24}\times \frac{96}{91}=\frac{25+h}{60}$

$\Rightarrow \frac{13}{24}\times \frac{96}{91}=\frac{25+h}{60}$

$\Rightarrow \frac{4}{7}=\frac{25+h}{60}$

$\Rightarrow 240=175+7h$

$\Rightarrow 7h=65$

$\Rightarrow h=\frac{65}{7}=9.29$

$\therefore h=9.29$