Question

A vertical stick $12m$ long casts a shadow $8m$ long on the ground. At the same time a tower casts the shadow $40m$ long on the ground. Determine the height of the tower.

• A. $50m$
• B. $60m$
• C. $40m$
• D. None of these

Answer 1

The correct option is B $60m$

In $△ABC$ and $△DEF$

$\angle A=\angle D={90}^{\circ }$

Since the tower and the stick cast their respective shadows at the same time on the ground,

So, $\angle C=\angle F$

$\therefore △ABC\sim △DEF$ ....(by AA similarity)

$\frac{AB}{DE}=\frac{AC}{DF}\Rightarrow \frac{12}{x}=\frac{8}{40}$

$\Rightarrow x=60m$