Question

A boy $2m$ long casts a shadow $1m$ long on the plane ground. At the same time, a tower casts a shadow $5m$ long on the ground. Find the height of the tower (in m).

Answer 1

Let $DE$ be the boy, $AB$ be height of tower.
$FE$ and $BC$ are the shadows of boy and tower respectively.

$BC=5m$

$DE=2m$

$FE=1m$

In both the cases, angle of elevation remains same.

Hence, $\angle DFE=\angle ACB$

$\tan \angle DFE=\tan \angle ACB$

$\frac{DE}{FE}=\frac{AB}{BC}$

$AB=5\times \frac{2}{1}=10m$