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The figure shows an overhead view of a corridor with a plane mirror MN mounted at one end. A burglar B sneaks along the corridor directly towards the centre of the mirror. If d = 3 m , how far from the mirror will the burglar be when the security guard S can first see him in the mirror?

Options

  1. A3.0   m
  2. B4.5   m
  3. C6.0   m
  4. D1.5   m

Correct answer

D. 1.5   m

Step-by-step solution

tan ⁡ θ = x MN 2 (in the smaller triangle) tan ⁡ θ = 3   m 3   m (in the bigger triangle) ∴       x 1.5 = 3 3 ∴       x = 1.5   m

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