A vertical pole 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) $40\text{ m}$
(b) $42\text{ m}$
(c) $36\text{ m}$
(d) $48\text{ m}$
Step-by-Step Solution
Key Concept: Similar triangles: $\dfrac{h_{pole}}{s_{pole}} = \dfrac{h_{tower}}{s_{tower}} \Rightarrow \dfrac{6}{4} = \dfrac{h}{28} \Rightarrow h = \dfrac{6 \times 28}{4} = 42\text{ m}$.
$\dfrac{6}{4} = \dfrac{h}{28} \Rightarrow h = 6 \times 7 = 42\text{ m}$. [1.0 Mark]
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Evaluating $h = 42\text{ m}$: 1.0 Mark
Correct Answer: $42\text{ m}$