Question

One chimney is $30\,m$ higher than another. A person standing at a distance of $100\,m$ , from the lower chimney observes their tops to be in line and inclined at an angle of tan $\left(\tan\right)^{- 1}\left(0 . 6\right)$ to the horizon. Then find the distance of the person from the higher chimney.

Answer 1

Let $BE=xm$

In $\Delta AEB,$ we get
$\tan\theta =\frac{30}{x}$
$\Rightarrow \tan\theta =0.6=\frac{30}{x}$
$\Rightarrow x=50$
Hence, the distance between person and chimney is
$=100+50=150\,m$