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Grade 12 · Trigonometry
Three-Dimensional Trigonometry (Grade 12)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    In the diagram below, calculate the size of DB̂C.
    (2)
    ABCD40°65°CD = 30 m32°hAB is vertical; B, C and D lie in the same horizontal plane
  2. 2
    In the diagram below, calculate the length of BC.
    (2)
    ABCD40°65°CD = 30 m32°hAB is vertical; B, C and D lie in the same horizontal plane
  3. 3
    In the diagram below, calculate the height of the pole AB.
    (2)
    ABCD40°65°CD = 30 m32°hAB is vertical; B, C and D lie in the same horizontal plane
  4. 4
    Why is AB̂C = 90° in the diagram below?
    (2)
    ABCD40°65°CD = 30 m32°hAB is vertical; B, C and D lie in the same horizontal plane
  5. 5
    Which triangle should you solve first in a 3-D problem?
    (2)
  6. 6
    An angle of elevation is measured from which direction?
    (2)
  7. 7
    Calculate the area of △BCD given BC = 19,96 m, CD = 30 m and BĈD = 65°.
    (2)
    ABCD40°65°CD = 30 m32°hAB is vertical; B, C and D lie in the same horizontal plane
  8. 8
    Can the sine rule be applied to a three-dimensional figure as a whole?
    (2)
    ABCD40°65°CD = 30 m32°hAB is vertical; B, C and D lie in the same horizontal plane
TOTAL: 16 marks
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