Question

A vertical stick $20m$ long casts a shadow $10m$ long on the ground,

At the same time a tower casts a shadow $50m$ long on the ground, the height of the tower is?

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

Answer 1

The correct option is B

$100m$

Find the height of the tower.

Draw the diagram according to the given data.

In the diagram, $BC$ will be the height of the stick, $CA$ will be the length of the shadow cast by the sick. $EA$ is the length of the shadow cast by the tower and $DE$ will be the height of the tower.

In $\Delta ABC\&\Delta AD{E}_{}$

$\angle BCA=\angle DEA={90}^o$ [Each is ${90}^o$ at to the ground]

$\angle BAC=\angle DAE$ [common angle]

$\angle CBA=\angle EDA$ [the sum will cast light at equal angles]

Hence, by $AAA,\Delta ABC~\Delta ADE$

$$\begin{gathered} \Rightarrow \frac{CA}{BC}=\frac{EA}{DE} \\ \Rightarrow \frac{10}{20}=\frac{50}{DE} \\ \Rightarrow DE=100 \end{gathered}$$

Hence, the height of the tower is $100m$.