Sine and Cosine Rule Explained

This PDF displays the sine and cosine rules for calculating missing angles and lengths in non-right-angled triangles, as well as the sine rule for the area of any triangle. All higher-tier students must know these formulae at GCSE.

The sine and cosine rules are essential for solving non-right-angled triangles in trigonometry.
This printable teaching resource provides clear explanations and worked examples, making it an ideal reference for students learning how and when to apply these rules.

When to Use the Sine and Cosine Rule?

• ✅ Sine Rule: When you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).
• ✅ Cosine Rule: When you have two sides and the included angle (SAS) or all three sides (SSS) and need to find an angle.

Sine Rule:

a / sin A = b / sin B = c / sin C

Used to find missing sides or angles when dealing with non-right-angled triangles.

Cosine Rule:

a² = b² + c² – 2bc cos A

Used when you have two sides and the included angle or all three sides and need to find an angle.

Finding a Missing Angle Using Cosine Rule:

cos A = (b² + c² – a²) / 2bc

Area of a Triangle Using Sine Rule:

Area = ½ × a × b × sin C

Helps find the area when two sides and the included angle are known.

Why Use This Resource?

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Browse our extensive collection of worksheets, tailored to help students master trigonometry, sine rule, cosine rule, and triangle calculations. All worksheets are downloadable in PDF format, ensuring easy access for classroom and home use!