Key Terms
- Sine rule: Connects any side with its OPPOSITE angle
- Matched pair: A side and its directly opposite angle (e.g. side a and angle A)
- Non-right-angled triangle: A triangle with no 90° angle
- Ambiguous case: When given ASS (two sides + non-included angle), two triangles may be possible
Must-Know Facts
- Use the sine rule when you have a MATCHED PAIR plus one more piece of information
- Side a is ALWAYS opposite angle A (same letter)
- To find a side: use a/sin A = b/sin B
- To find an angle: flip to sin A/a = sin B/b, then use sin⁻¹
- The three angles of any triangle sum to 180°
Key Formulas
- Find side: a/sin A = b/sin B = c/sin C
- Find angle: sin A/a = sin B/b = sin C/c
- Use when: AAS, ASA (have angle + opposite side)
Common Mistakes
- Wrong pairing: Each side must pair with the angle directly opposite it — a pairs with A, b with B, c with C
- Ambiguous case: When finding an angle with sine rule, there may be two possible answers (acute and obtuse) — check the context
- Using sine rule when cosine rule needed: Sine rule needs an angle-opposite-side pair — use cosine rule for SAS or SSS
- Calculator mode: Must be in degrees mode for GCSE problems
This topic summary covers Knowledge Organiser: The Sine Rule within Sine Rule for GCSE Mathematics. Revise Sine Rule in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Sine Rule
Which of the following is the sine rule?
Explain what is meant by the ambiguous case of the sine rule, and state when it can occur.
Quick recall flashcards
Sine Rule
a/sinA = b/sinB = c/sinC. Use when you have a matched pair (side with opposite angle).
Sine Rule
a/sin A = b/sin B = c/sin C