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CAIE IGCSE Mathematics Three-Dimensional Trigonometry

Practise identifying useful right triangles in solids and using Pythagoras or trigonometry for space diagonals and line-to-plane angles.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

Exam points

  • calculate a face diagonal before using it with the third dimension in a second right triangle
  • identify the projection of a line onto the plane when finding the angle between line and plane
  • use Pythagoras or a trigonometric ratio with the derived 3D triangle and retain intermediate accuracy

E6.6.1 in 3D Carry out calculations and solve problems in three dimensions question 1

[Maximum number: 5]
NOT TO SCALE

NOT TO SCALE

The diagram shows triangle ABC on horizontal ground.
AC=15 m,BC=8 mA C=15 \mathrm{~m}, B C=8 \mathrm{~m} and AB=20 mA B=20 \mathrm{~m}.
BP and CQ are vertical poles of different heights.
BP=3 mB P=3 \mathrm{~m} and CQ=4 mC Q=4 \mathrm{~m}.
AQ and PQ are straight wires.

Another straight wire connects A to the midpoint of PQ.

Calculate the angle between this wire and the horizontal ground.

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