A vertical stick of length $6\text{ m}$ casts a shadow $4\text{ m}$ long on the ground and at the same time a tower casts a shadow $28\text{ m}$ long. The height of the tower is:
(a) $36\text{ m}$
(b) $42\text{ m}$
(c) $48\text{ m}$
(d) $54\text{ m}$
Step-by-Step Solution
Key Concept: At the same time, sun's elevation is equal, making the right-angled triangles formed by stick and tower similar.
$\dfrac{\text{Height of stick}}{\text{Shadow of stick}} = \dfrac{\text{Height of tower}}{\text{Shadow of tower}} \Rightarrow \dfrac{6}{4} = \dfrac{h}{28}$. [0.5 Mark]
$h = \dfrac{6 \times 28}{4} = 6 \times 7 = 42\text{ m}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Setting up similarity ratio: 0.5 Mark
Solving for height $h = 42\text{ m}$: 0.5 Mark
Correct Answer: $42\text{ m}$