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A tower leans towards west making an angle α with the vertical. The angular elevation of B , the top most point of the tower, is 75 o as observed from a point C due east of A at a distance of 20 units. If the angular elevation of B  from a point due east of C at a distance of 20 units from C is 45 o , then tan ⁡ α is equal to

Options

  1. A3 + 1 2
  2. B3 + 1 3 - 1
  3. C3 - 2 3
  4. D3 - 1 2

Correct answer

C. 3 - 2 3

Step-by-step solution

By m – n theorem, we have 40 cot ⁡ 75 o = 20 cot ⁡ 45 o - 20 cot ⁡ π 2 + α ⇒ 40 2 - 3 = 20 + 20 tan ⁡ α ⇒ tan ⁡ α = 3 - 2 3

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