CAIE IGCSE Mathematics Sine and Cosine Rule Problems

Practise selecting and applying sine or cosine rules to calculate sides and angles in non-right-angled triangles, including obtuse results.

Exam points

use the sine rule when a known side–opposite-angle pair is available in the triangle
use the cosine rule for three sides or two sides with their included angle
check the ambiguous sine case and select an obtuse angle when the diagram or context requires it

[Maximum number: 4]

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.

Show that angle $ACB=117.5^\circ$ , correct to 1 decimal place.

$\cos ACB=\frac{15^2+8^2-20^2}{2\times15\times8}$
M2
117.54 to 117.55
A2
A1 for $-\frac{37}{80}$ , $-\frac{111}{240}$ , or -0.4625

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E6.5.1 Use the sine and cosine rules in calculations involving lengths and question 1