Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
The cosine rule (law of cosines)
Trigonometry
CCSS HSG.SRT.D.10CCSS HSG.SRT.D.11England: GCSE Higher Geometry
Objective and success criteria
Students will: The cosine rule (law of cosines).
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Trigonometric ratios: SOH CAH TOA; Pythagoras' theorem
Leads to: Find a side with the cosine rule
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Trigonometric ratios: SOH CAH TOA; Pythagoras' theorem). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: The cosine rule (law of cosines). Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: In triangle ABC, b = 16 cm, c = 9 cm and angle A = 38°. Find side a to 1 decimal place.
- Step 1: a² = 256 + 81 − 2 × 16 × 9 × cos 38°
- Step 2: a² ≈ 110.053
- Step 3: a ≈ 10.5 cm
- Answer: 10.5
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- In triangle ABC, b = 11 cm, c = 20 cm and angle A = 86°. Find side a to 1 decimal place. → 22.1Prompt: Cosine rule: a² = b² + c² − 2bc cos A.
- A triangle has sides a = 12, b = 5 and c = 8. Find angle C (opposite side c) to 1 decimal place. → 29Prompt: Rearranged cosine rule: cos C = (a² + b² − c²) / 2ab.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A triangle has sides a = 6, b = 12 and c = 9. Find angle C (opposite side c) to 1 decimal place. → 46.6Prompt: Rearranged cosine rule: cos C = (a² + b² − c²) / 2ab.
- In triangle ABC, b = 19 cm, c = 20 cm and angle A = 76°. Find side a to 1 decimal place. → 24Prompt: Cosine rule: a² = b² + c² − 2bc cos A.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Trigonometric ratios: SOH CAH TOA.
- Use concrete materials: scientific calculators.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Find a side with the cosine rule.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder