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      Question

      A long metallic cable is stretched from a point P on the

      ground to the top of a cliff, forming an angle of 30 ° with the horizontal ground. The total length of the cable is 450 √3 meters. Determine the horizontal distance between point P and the base of the cliff.
      A 325√3 metres Correct Answer Incorrect Answer
      B 675 metres Correct Answer Incorrect Answer
      C 725 metres Correct Answer Incorrect Answer
      D 525 metres Correct Answer Incorrect Answer

      Solution

      In the given figure, let 'A' and 'B' represent the foot and the top of the cliff, respectively. In right rPAB, cos30o = (AP/PB) Or, (√3/2) = (AP/450√3) So, PA = (450√3) X (√3/2) = 675 metres Therefore, distance between point 'P' and the foot of the cliff is 675 metres

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