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

Question

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, 5 3 2 m, 5 3 2 m, 5 2 3 m, None of these

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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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