Question

A $150$ cm tallboy stands at a distance of $8$ m from a lamp post and casts a shadow of $2$ m. Find the height of the lamp post.

Answer 1

Let the height of the lamp post be $h$.

Therefore, from the above figure,

$\tan \theta =\frac{1.5}{2}$ {$150cm=1m$}

$\tan \theta =\frac{h}{8+2}$

Equating both we get,

$\Rightarrow \frac{1.5}{2}=\frac{h}{10}$

$\Rightarrow h=\frac{1.5\times 10}{2}=7.5m$

$h=7.5m$