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The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 30 ° . After walking 120   m towards it on a level ground, the angle of elevation is found to be 60 ° . Then the height of the object (in metres) is

Options

  1. A120
  2. B60 3
  3. C120 3
  4. D60

Correct answer

B. 60 3

Step-by-step solution

In ∆ C A D , tan ⁡ 30 ° = C D A C ⇒ 1 3 = h 120 + x ⇒ 3 h = 120 + x ...(i) and in ∆ C B D , tan ⁡ 60 ° = C D B C ⇒ 3 = h x ⇒ h = 3 x ...(ii) From Eqs. (i) and (ii), we get, x = 60 m On putting x = 60 in Eq.(i), we get h = 60 3 m

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