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      Question

      A vertical pole and a vertical tower are standing on the

      same level ground. Height of the pole is 15 metres . From the top of the pole the angle of elevation of the top of the tower and angle of depression of the foot of the tower are 60° and 30° respectively. The height of the tower is:
      A 50 m Correct Answer Incorrect Answer
      B 40 m Correct Answer Incorrect Answer
      C 60 m Correct Answer Incorrect Answer
      D 45 m Correct Answer Incorrect Answer

      Solution

      AB = Pole CE = Tower AB = 15 m In ∆ABE tan30° = AB/BE 1/√3 = AB/BE 1/√3 = 15/BE BE = 15√3 m AD = BE = 15√3 In ∆ACD tan60° = CD/AD ⇒ √3 = CD/(15√3) ⇒ CD = 45 CD + DE = 45 + 15 ⇒ 60 m

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