ChalkHour

Year 11 Maths: Sine and cosine rules lesson pack

A complete, ready-to-teach GCSE lesson on sine and cosine rules. Below is a real sample of what ChalkHour makes: the full pack adds three levels of worksheet, model answers, a teaching explainer and print-ready PDF and Word files.

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Real sample

The Sine and Cosine Rules

A comprehensive lesson for Year 11 students on using the Sine and Cosine rules to find missing lengths and angles in non-right-angled triangles, moving from basic application to complex multi-step problems.

Learning objectives

  • Identify when to use the Sine Rule or the Cosine Rule in non-right-angled triangles.
  • Calculate missing sides and angles using the Sine Rule.
  • Calculate missing sides and angles using the Cosine Rule.
  • Apply trigonometry to solve multi-step problems in context.

Lesson plan (60 minutes)

  1. Starter · 5 min

    Do Now: Recall Pythagoras and SOH CAH TOA for right-angled triangles. Check understanding of labeling sides opposite angles.

  2. Introduction 1 · 10 min

    Introduction to Sine Rule: When to use it (AAS or SSA) and the formula. Worked example on finding a side.

  3. Introduction 2 · 10 min

    Introduction to Cosine Rule: When to use it (SAS or SSS) and the formula. Worked example on finding a side.

  4. Guided Practice · 5 min

    Guided Practice: Students attempt two short problems on mini-whiteboards to decide which rule to use.

  5. Independent Practice · 20 min

    Independent Practice: Students work through differentiated worksheets (Support, Core, or Stretch).

  6. Plenary · 10 min

    Plenary: 8-question multiple choice quiz to assess learning and address misconceptions.

Key vocabulary

Opposite Pair
A side and its opposite angle (e.g., side 'a' and angle 'A'). Necessary for the Sine Rule.
Included Angle
Two sides and the angle formed between them. Requires the Cosine Rule to find the third side.
Sine Rule
a/sinA = b/sinB = c/sinC. Used for triangles without a right angle.
Cosine Rule
a² = b² + c² - 2bc cos A. Used for triangles without a right angle.
Opposite Side
The side directly across from a specific angle.

Core worksheet (first questions)

  1. In triangle ABC, A = 42°, B = 61°, and b = 12 cm. Find side x (side a).
  2. In triangle PQR, P = 110°, side p = 10 cm, side q = 7 cm. Find angle θ (angle Q).
  3. Find length AC in a triangle where AB = 5 cm, BC = 8 cm, and angle B = 60°.
  4. In triangle XYZ, XY = 8 cm, YZ = 10 cm, and XZ = 7 cm. Find angle Y (angle P in model).

Quiz (sample)

  1. 1. Complete the Sine Rule: a / sin A = ...

    • A. a / cos A
    • B. b / sin B
    • C. c / tan C
    • D. 1/2 ab sin C

  2. 2. Which is the correct Cosine Rule for finding side 'a'?

    • A. a² = b² + c² + 2bc cos A
    • B. a² = b² + c² - 2bc sin A
    • C. a² = b² + c² - 2bc cos A
    • D. a = b + c - cos A

  3. 3. If you know two sides and the included angle, which rule should you use?

    • A. Sine Rule
    • B. Cosine Rule (SAS)
    • C. Pythagoras' Theorem
    • D. SOH CAH TOA

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