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, The Height Of The Tower Is ?(A) 25m (B) 100m (C) 120m (D) 200m

The correct answer is (B) 100m

In \( \Delta ABC and \Delta ADE \),

\(\angle BCA = \angle DEA = 90^{\circ} \) [Each are at 90o to the ground] \(\angle BAC = \angle DAE \) [common angle] \(\angle CBA = \angle EDA \)[Since the sum will cast light a equal angles]

Hence, \(AAA, \Delta ABC \sim \Delta ADE \) \(\Rightarrow \frac{BC}{CA} = \frac{DE}{EA} \) \(\Rightarrow \frac{20}{10} = \frac{DE}{50} \) \(\Rightarrow DE = 100 \)

Therefore,the height of the tower is 100m.

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