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      Question

      A 16-meter-long rope is stretched from the ground to the

      top of a house, forming a 30° angle with the ground. Determine the height of the house.
      A 8 m Correct Answer Incorrect Answer
      B 16 m Correct Answer Incorrect Answer
      C 16/√3 m Correct Answer Incorrect Answer
      D 16√3 Correct Answer Incorrect Answer

      Solution

      Image

      Let AB be the height of the house and AC be the length of the rope

      In right ΔABC

      sin30° = (AB/AC)

      Or, (1/2) = (AB/16)

      Or, AB = (16/2) = 8

      Therefore, the height of the house = 8 metres

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