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      Question

      From a point on the ground, the angle of elevation to

      the top of a tree is 30 degrees. If you walk 20 feet closer to the tree, the angle of elevation becomes 45 degrees. What is the height of the tree?
      A 20√2 feet Correct Answer Incorrect Answer
      B 10(√3 + 1) feet Correct Answer Incorrect Answer
      C 20(√2 - 1) feet Correct Answer Incorrect Answer
      D 40 feet Correct Answer Incorrect Answer

      Solution

      Let the height of the tree be h feet. Let the initial distance from the point on the ground to the tree be x feet. From the first angle of elevation, we have tan(30) = h/x From the second angle of elevation, we have tan(45) = h/(x - 20) Since tan(45) = 1, we have 1 = h/(x - 20), so h = x – 20 Substituting h into the first equation: tan(30) = (x - 20)/x Answer: (b)

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