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

Answer 1

Answer: (A)

$100m$

In $\Delta ABC$ & $\Delta ADE$

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

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

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

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

$\Rightarrow \frac{BC}{CA}=\frac{DE}{EA}$

$\Rightarrow \frac{20}{10}=\frac{DE}{50}$

$\Rightarrow DE=100$

$\therefore$ The height of the tower is $100$m.