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The sine rule and cosine rule solve triangles that are not right-angled, finding missing sides and angles, along with the area formula ½ab sin C. This topic covers choosing the right rule and the ambiguous case. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Use the sine rule when you have a matching side and angle, and the cosine rule when you have three sides or two sides and the angle between them. Area is half ab sin C. Where the sine rule gives an angle, check whether the obtuse alternative also fits.
Before you start
The prerequisite is right-angled trigonometry. Examined in Pure 1. From here the path runs to non-right-angled triangles and area. The topic sits within Trigonometry.
What you learn
The sine and cosine rules extend trigonometry to any triangle — not just right-angled ones. The obtuse alternative is its supplement, 180°-θ, because sinθ= sin (180°-θ). The angle in the area formula must be the one between the two sides used. The course works through cosine rule — finding a side, cosine rule — finding an angle, sine rule and the obtuse case, area of a triangle, and working back and multi-step problems. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Sine & Cosine Rules belongs to Trigonometry and is met in the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Nearby topics in the same strand are Solving Trig Equations, Trig Graphs & Transformations, Trig Identities (C12) and Trig Ratios & Exact Values. The Trigonometry revision engine gives you as many extra questions as you want, tracked on your skill tree.
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