IB Math AI HL — 2D and 3D trigonometry

Key Idea: Topic 3.2 covers the three core tools of non-right-angle trigonometry: the sine rule, the cosine rule, and the triangle area formula. These handle any triangle when you don't have a right angle. The key is recognising which rule to use based on what information you are given.

✅ Right-angle trig: SOH CAH TOA

📐 Non-right-angle rules

Example: Sine rule: Triangle with A = 35°, a = 8, B = 72°. Find b. b/sin 72° = 8/sin 35° → b = 8 × sin72°/sin35° = 13.3 (3 s.f.) Cosine rule (SAS): a = 7, b = 10, C = 50°. Find c. c² = 7² + 10² − 2(7)(10)cos50° = 49 + 100 − 140(0.643) = 59.0 → c = 7.68 Area: Two sides 6 and 9, included angle 40°. Area = ½ × 6 × 9 × sin40° = 17.4 cm²

Ambiguous case of the sine rule: when you have SSA (two sides and a non-included angle), there can be two valid triangles. Check whether 180° − θ is also a valid solution. For 3D trig problems: identify the 2D triangle cross-section inside the 3D shape. Then apply the appropriate 2D rule.

Paper 1 (GDC allowed): Label all sides and angles on your diagram before starting. State which rule you're using. Paper 2 (GDC allowed): The GDC handles all calculations — focus on setting up the correct formula and substituting accurately. Round intermediate values carefully (don't round mid-calculation).