Sine rule

a/sin A = b/sin B = c/sin C for any triangle. CAPS Grade 11 definition, worked example and related trigonometry practice.

a/sin A = b/sin B = c/sin C for any triangle.

Definition

The sine rule links each side of a triangle to the sine of the angle opposite it: a/sin A = b/sin B = c/sin C. Use it when you know a side and its opposite angle, plus one more side or angle.

Worked example

In △ABC, a = 9, Â = 65° and B̂ = 40°: b = 9 sin 40° ÷ sin 65° ≈ 6.38.

To find an angle, use the reciprocal form: sin B / b = sin A / a.

Where it appears in the exam

Sine rule is part of the trigonometry section of CAPS Grade 11 Mathematics and is examined in Paper 2 of the November exam.

Step-by-step method

  1. Label the sides with lower-case letters opposite their angles.
  2. Check that you know one side–angle pair.
  3. Set up the ratio with the unknown.
  4. Solve, and round as instructed.

Common mistake

Pairing a side with an angle that isn't opposite it.

Related trigonometry terms

Frequently asked questions

What does sine rule mean in Grade 11 Maths?

The sine rule links each side of a triangle to the sine of the angle opposite it: a/sin A = b/sin B = c/sin C. Use it when you know a side and its opposite angle, plus one more side or angle.

Which paper tests sine rule in Grade 11?

Sine rule belongs to the Trigonometry section of CAPS Grade 11 Mathematics, which is examined in Paper 2 of the November exam.

How do I practise questions involving sine rule?

Snap a question that uses sine rule into Snap&Learn with your grade set to Grade 11, or work through the Grade 11 topic guide and practice papers.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.