Which triangle formula (NF)

A standard method from Trigonometry (2-D): the steps and worked examples.

Steps

You know	Use
2 sides and the angle between them; want the third side	cosine formula: c² = a² + b² − 2ab cos C
3 sides; want an angle	cosine formula: cos C = (a² + b² − c²)/(2ab)
2 angles and a side, or a side and its opposite angle plus one more	sine formula: a/sin A = b/sin B = c/sin C
2 sides and the included angle; want the area	½ab sin C
3 sides; want the area	Heron: √[s(s − a)(s − b)(s − c)], s = (a + b + c)/2

List what you know: which sides, which angles, and whether the known angle is between the two known sides.
Match it to a row of the table and write the formula before substituting.
After each new value, check the table again for the next step. An angle found with the sine formula may also have an obtuse answer (180° − θ).

Example 1: NF: which triangle formula? A triangle has sides 7, 8 and 9. Find its largest angle.

3 sides, want an angle → cosine formula
the largest angle C is opposite the longest side, 9
cos C = (7² + 8² − 9²)/(2 × 7 × 8) = 32/112
C ≈ 73.4°

For the whole topic, read Trigonometry (2-D): key points, common mistakes and how the DSE tests it.