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      Question

      A tree of height 'h' meters is partially bent at a

      certain point above the ground, causing its top to touch the ground at a distance of 12 meters from its base. The bent portion forms a 45° angle with the ground. Determine the value of 'h'.
      A (12 + 12√2) Correct Answer Incorrect Answer
      B 12 Correct Answer Incorrect Answer
      C 12√2 Correct Answer Incorrect Answer
      D (12 - 12√2) Correct Answer Incorrect Answer

      Solution

      Image Let the point from which the tree was bent be 'A'.In right triangle ABC, we havetan 45o = (AB/BC)So, AB = BC = 12 metresUsing Pythagoras theorem,AC2 = AB2 + BC2Or, AC2 = 122 + 122 = 144 + 144 = 288Or, AC = 12√2 metres (Since, height cannot be negative therefore, we will take positive root only)Length of the tree = h = (12√2 + 12) metres

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