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      Question

      A vertical pole and a vertical tower are on the same

      level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m).
      A 24√3(√3+1) Correct Answer Incorrect Answer
      B 24(√3+1) Correct Answer Incorrect Answer
      C 72 Correct Answer Incorrect Answer
      D 19 Correct Answer Incorrect Answer

      Solution

      Let, the height of the pole (AB) = CD = x m So, the height of ED = (76 - x) m So, In ΔACD, tan 30° = CD/AD ⇒ 1/√3 = x/AD ⇒ AD = √3x .....(1) In ΔAED, tan 60° = ED/AD ⇒ √3 = (76 - x)/√3x ⇒ 76 - x = 3x ⇒ 3x + x = 76 ⇒ 4x = 76 ⇒ x = 76/4 = 19 ∴ The height (in m) of the pole is 19 m

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