Solution of Triangles
Solution of triangles covers the sine rule, the cosine rule and the area formula, plus bearings and the ambiguous case. SPM tests choosing the correct rule from the given information and interpreting obtuse angles correctly.
Core rules
Sine rule: a/sin A = b/sin B = c/sin C. Cosine rule: a² = b² + c² − 2bc cos A. Area = ½ab sin C, where C is the included angle. Use the sine rule when a matching side and angle are available; use the cosine rule when three sides are known or when two sides and the included angle are known.
Worked example
In a triangle, b = 5 cm, c = 7 cm and A = 60°. Then a² = 5² + 7² − 2(5)(7) cos 60° = 25 + 49 − 35 = 39, so a = 6.245 cm. The area is ½(5)(7) sin 60° = 15.16 cm².
Traps
Using sin instead of cos in the cosine rule; using a non-included angle in the area formula; ignoring the ambiguous case when given two sides and a non-included angle; leaving the calculator in degree mode.