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Kritika once standing near the main gate of her building which is of 11 stories found the angle of elevation to be 30° to the top of the cable antenna which is fixed on her terrace. She moved 50m in a straight line parallel to her feet towards the antenna and she found that angle of elevation changed to 45°. Find the height of the antenna from the ground?

Kritika once standing near the main gate of her building which is of 11 stories found the angle of elevation to be 30° to the top of the cable antenna which is fixed on her terrace. She moved 50m in a straight line parallel to her feet towards the antenna and she found that angle of elevation changed to 45°. Find the height of the antenna from the ground? Correct Answer 25 (√3 + 1) 

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⇒ In ΔCDB, ∠CDB = 45°

⇒ Now since, tan 45° = CB/DB = 1

⇒ CB = DB = x

⇒ Now, tan 30° = CB/AB

⇒ 1/√ 3 = x/(50 + x)

⇒ (50 + x) = √3 × x

⇒ 50 = x (√3 – 1)

⇒ x = 50 / (√3 – 1)

⇒ x = 50/(√3 – 1) × (√3 + 1) /(√3 + 1)

⇒ x = 25 (√3 + 1)

∴ Answer is 25 (√3 + 1)

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