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8 marksMeasurement Problems

CSEC Mathematics · May/June 2004 · Paper 2 · Question 12(b)(ii)b)

In this question, use π = 3.14 and assume the earth to be a sphere of radius 6 370 km. The diagram shows a sketch of the earth with the Greenwich Meridian and the Equator labelled. The towns A and B are both on the circle of latitude 24° N. The longitude of A is 108° E and the longitude of B is 75° E.

Calculate, correct to the nearest kilometre, the shortest distance between A and B, measured along the circle of latitude 24° N.

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Other parts of this question

  1. 12(a)(i)Express in fractional or surd form the value of cos θ.[7 marks]
  2. 12(a)(ii)Show that the area of triangle CDE is 150√3 square units, where CD = 30 units and DE = 20 units.[7 marks]
  3. 12(a)(iii)Calculate the length of the side EC.[7 marks]
  4. 12(b)(i)Copy the sketch above of the earth and insert the points A and B on your diagram.[8 marks]
  5. 12(b)(ii)a)Calculate, correct to the nearest kilometre, the radius of the circle of latitude 24° N.[8 marks]

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