Question

A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. Find the height of the tower.

• A. 25 m
• B. 100 m
• C. 120 m
• D. 200 m

Answer 1

The correct option is B

100 m

Figure 4

Let the height of the tower be $x$ metres.

In $\Delta ABC$ and $\Delta DEF$
$\angle A=\angle D$
$\angle B=\angle E={90}^{\circ }$

Since the two triangles are similar by AA similarity criterion, we have
$\frac{x}{50}=\frac{20}{10}$

$x=100m$