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Edexcel IGCSE·Maths·IGCSE Higher Mathematics

The Sine & Cosine Rules

14 min read

Trigonometry in non-right-angled triangles: the sine rule, the cosine rule, the area formula, and choosing the right tool.

For triangles that are not right-angled, use the sine and cosine rules. Sides a,b,ca,b,ca,b,c are opposite angles A,B,CA,B,CA,B,C.

The sine rule

asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}sinAa​=sinBb​=sinCc​ Use when you have a side and its opposite angle, plus one more side or angle. (To find an angle, flip it: sin⁡Aa=sin⁡Bb\frac{\sin A}{a}=\frac{\sin B}{b}asinA​=bsinB​.)

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