The Sine Rule
Grade 6When to use the sine rule
The sine rule works in any triangle — not just right-angled ones. Use it when you have a matching side-angle pair (one side and its opposite angle), plus one more piece of information.
a/sin A = b/sin B = c/sin C
Lowercase letters are sides; uppercase are the opposite angles. You can also flip the fractions: sin A/a = sin B/b = sin C/c — useful when finding an angle.
Setting it up
Label the triangle: call the known side–angle pair a and A. Then use b/sin B = a/sin A (or the angle version) to find the unknown.
Use the side-finding version (a/sin A = ...) when you need a length. Use the angle-finding version (sin A/a = ...) when you need an angle. Two versions, same rule.
Worked example
EXAMPLE
In triangle ABC, angle A = 42°, angle B = 73°, and side a = 9 cm. Find side b.
b/sin B = a/sin A. b = a × sin B / sin A = 9 × sin 73° / sin 42° = 9 × 0.9563 / 0.6691 ≈ 12.9 cm (to 3 s.f.).
