4.8.5

Sine Rule

Test yourself

Sine and Cosine Rules

We can use the sine and cosine rules to calculate angles and lengths in triangles.

Illustrative background for Labelling trianglesIllustrative background for Labelling triangles ?? "content

Labelling triangles

  • Use lowercase letters for the sides and capital letters for the angles opposite each side.
Illustrative background for Swapping A, B and CIllustrative background for Swapping A, B and C ?? "content

Swapping A, B and C

  • Note that the cosine rule can be written for the other angles too:
    • c2 = a2 + b2 - 2ab cos C
    • b2 = a2 + c2 - 2ac cos B

Sine and Cosine Rules

We can use the sine and cosine rules to calculate angles and lengths in triangles.

Illustrative background for Labelling trianglesIllustrative background for Labelling triangles ?? "content

Labelling triangles

  • You need to label the angles and sides of triangles for the sine and cosine rules.
  • Lowercase letters are used for the sides and capital letters for the angles opposite each side.
Illustrative background for Swapping A, B and CIllustrative background for Swapping A, B and C ?? "content

Swapping A, B and C

  • A, B and C (and a, b and c) can be swapped to make sure you can use the equation for the sine and cosine rule.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

Go student ad image

Unlock your full potential with GoStudent tutoring

  • Affordable 1:1 tutoring from the comfort of your home

  • Tutors are matched to your specific learning needs

  • 30+ school subjects covered

Book a free trial lesson