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A flat mirror lies on level ground between a boy and a tower. The boy, whose eyes are 1.6 m above the ground, stands 2 m from the mirror and sees the very top of the tower reflected in it. The mirror is 25 m from the foot of the tower. How tall is the tower?

Competition practiceGeometry
  • A31.25 m
  • B20 m
  • C16 m
  • D40 m

Step-by-Step Solution

A mirror reflects at equal angles, so the ray makes the same angle with the ground on both sides. That gives two similar right triangles: eye height over its ground distance equals tower height over its ground distance. So , and m. Inverting the ratio gives m, which is the common error.
Answer: B) 20 m

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