Question

A student wants to determine the height of a flagpole. He placed a small mirror on the ground so that he can see the reflection of the top of the flagpole. The distance of the mirror from him is $0.5m$ and the distance of the flagpole from the mirror is $3m$. If his eyes are $1.5m$ above the ground level, then find the height of the flagpole. (The foot of student, mirror and the foot of flagpole lie along a straight line)

Answer 1

Let $C$ is point of reflection in $△ABC$ and $△EDC$

$\angle ABC=\angle EDC\left({90}^{\circ }\right)$

$\angle ACB=\angle ECD$ (reflexive angle)

By $AA$ symmetry

$△ABC\sim △EDC$

$\frac{AB}{ED}=\frac{BC}{DC}$

$\frac{1.5\times 3}{0.5}=ED$

$ED=9$

So height of pole is $9m$