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A tower A B leans towards west making an angle α with the vertical. The angular elevation of B , the top most point of the tower, is 6 0 o as observed from a point C due east of A at a distance of 10 ft from A . If the angular elevation of B from a point D due east of C at a distance of 20 ft from C is 4 5 o , then the value of 2 tan ⁡ α is equal to

Options

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

Correct answer

C. 3 - 1

Step-by-step solution

By m - n theorem, we have 30 cot ⁡ 60 o = 10 cot ⁡ 45 o - 20 c o t π 2 + α ⇒ 10 3 = 10 + 20 tan ⁡ α ⇒ 2 tan ⁡ α = 3 - 1

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