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. (2 marks)

Answer 1

Figure 4

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

In $\Delta ABC$ and $\Delta DEF$
$\angle A=\angle D$
$\angle B=\angle E={90}^{\circ }$ (1 mark)

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

$x=100m$ (1 mark)