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A flag - staff of 5 meters high stands on a building of 25 meters height. For an observer at a height of 30 meters, the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag - staff is

Options

  1. A5 3 2 m
  2. B5 3 2 m
  3. C5 2 3 m
  4. DNone of these

Correct answer

B. 5 3 2 m

Step-by-step solution

We have tan ⁡ α = 5 x and tan ⁡ 2 α = 30 x ∴ tan ⁡ 2 α = 30 5 cot ⁡ α ⇒ tan ⁡ 2 α = 6 tan ⁡ α

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