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A vertical pole 6 m tall casts a shadow 4 m long on level ground. At the same time of day a tower nearby casts a shadow 28 m long. How tall is the tower?

Competition practiceGeometry
  • A42 m
  • B18.7 m
  • C30 m
  • D56 m

Step-by-Step Solution

The sun's rays arrive at the same angle, so the pole with its shadow and the tower with its shadow form similar right triangles: height/shadow is the same for both. That ratio is 6/4 = 1.5, so the tower's height = m. Turning the ratio upside down gives ≈ 18.7 m, the classic slip.
Answer: A) 42 m

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