CAIE IGCSE Mathematics Two-Dimensional Triangle Problems

Practise combining Pythagoras and trigonometric ratios across connected two-dimensional triangles to calculate lengths, angles and distances.

Exam points

draw or identify the perpendicular that creates a useful right triangle in the 2D diagram
calculate a missing side or angle with Pythagoras, sine, cosine or tangent as appropriate
carry the intermediate value into the adjoining triangle without premature rounding

[Maximum number: 2]

NOT TO SCALE

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

Calculate the length of AQ.

15.5 or 15.52 to 15.53
M1 for $15^2+4^2$ oe

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E6.2.2 Solve problems in two dimensions using Pythagoras’ theorem and question 1