IB Maths: The Sine & Cosine Rules — FAQ

Start by labelling your triangle: which sides and angles do you know, and which are you finding? If you have two sides and the angle between them (SAS) or all three sides (SSS), use the cosine rule. If you have two angles and a side, or two sides and a non-included angle (SSA), use the sine rule.

The sine rule (a/sin A = b/sin B = c/sin C) links each side to its opposite angle, so use it when you already know one complete angle-side pair. The cosine rule (c² = a² + b² − 2ab cos C) handles SAS or SSS triangles, where no matching angle-side pair exists at all.

The ambiguous case happens when you're given two sides and a non-included angle (SSA) and use the sine rule to find another angle — your calculator gives one solution, but a second, obtuse solution (180° minus that angle) can also fit, producing two valid triangles. Always sketch to check which answer, or both, make sense.

You don't need the height — the area formula, Area = ½ab sin C, uses two sides and the included angle instead. It's printed in the IB formula booklet, so you substitute the two known sides and the angle between them, then evaluate on your calculator in the correct angle mode.

The biggest one I see marking mock papers: students mix up which rule fits which information, especially forgetting the cosine rule needs SAS or SSS. Others forget the ambiguous case entirely, round intermediate angles too early and lose accuracy marks, or leave their calculator in radian mode when the question's in degrees.

It depends on the course. In Maths AI, both Paper 1 and Paper 2 allow a calculator, so most sine/cosine rule work is numerical throughout. In Maths AA, Paper 1 is non-calculator, so you may need to leave an exact value (like cos C = ½) rather than a decimal, then simplify by hand.

Examiners award method marks for correctly substituting into the sine or cosine rule formula, even if your final numerical answer is wrong through a calculator slip. Write the formula first, substitute the actual values from the question, then simplify — jumping straight to a decimal answer risks losing the method mark entirely.

Yes — the sine rule, cosine rule and area formula sit in Topic 3, Geometry and trigonometry, for both Mathematics: analysis and approaches and Mathematics: applications and interpretation, at SL and HL. According to the IB's current Mathematics guides, first examined from 2021 and still the basis for the 2025 syllabus, the content and formulas are identical across both courses.

Not really — HL students use exactly the same sine rule, cosine rule and area formulas as SL, printed in the same formula booklet. What makes HL questions feel harder is context: sine and cosine rule steps get folded into vector geometry, 3D trigonometry or optimisation problems rather than tested in isolation.

No — the sine rule, both forms of the cosine rule, and the area formula are all printed in the IB Mathematics formula booklet under Geometry and trigonometry, for SL and HL alike. What you actually need to know is when to apply each one, since the booklet won't tell you that part.

Both courses weight this topic similarly — it's core SL content examined every session, so it matters whichever course your child takes. Maths AI tends to frame these questions in real-world contexts like surveying and bearings, while Maths AA leans more towards pure geometric problem-solving, often combined with algebra or trigonometric identities.

Targeted practice across all three triangle types (SSA, SAS, SSS) closes the gap faster than repeating one style of question over and over. Look for topic-specific practice that groups problems by which rule applies, then timed past-paper questions mixing sine/cosine rule steps into bearings and 3D problems — that's exactly what shows up on Paper 2.