Question

A man $1.8m$ tall stands at distance of $3.6m$ from a lamp post and casts a shadow of $5.4m$ on the ground. Find the height of the lamp post.

• A. $2m$
• B. $5m$
• C. $3m$
• D. $7m$

Answer 1

Answer: (C)

$3m$

Let $\theta$ be the unknown angle of elevation.
Let DF be the man and AB be the lamp post.
Considering the given figure.
$\tan \theta$
$=\frac{1.8}{5.4}$
$=\frac{x}{3.6}$
Hence
$x=\frac{\left(3.6\right).\left(1.8\right)}{5.4}$
$=1.2m$
Hence
The height of the lamp post is
$1.2m+1.8m$
$=3m$