Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Find an angle with the cosine rule
Trigonometry
CCSS HSG.SRT.D.11England: GCSE Higher Geometry
Objective and success criteria
Students will: Find an angle with the cosine rule.
- 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: Find a side with the cosine rule
Leads to: the next skill in this area.
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 (Find a side with the cosine rule). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- In triangle ABC, b = 9 cm, c = 19 cm and A = 40°. Find a to 1 decimal place. → 13.4Prompt: a² = b² + c² − 2bc cos A.
- Elena and Arjun cycle away from the same café along two straight paths with an angle of 144° between them. Elena rides 12 km and Arjun rides 29 km. How far apart are they? Give 1 decimal place. → 39.3Prompt: Sketch a triangle: two known sides and the angle between them.
- In triangle ABC, b = 18 cm, c = 14 cm and A = 92°. Find a to 1 decimal place. → 23.2Prompt: a² = b² + c² − 2bc cos A.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Find an angle with the cosine rule. 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: A triangle has sides a = 9, b = 10 and c = 6 cm. Find angle A (opposite a) to 1 decimal place.
- Step 1: cos A = (100 + 36 − 81)/120 ≈ 0.4583
- Step 2: A ≈ 62.7°
- Answer: 62.7
- 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.
- A triangle has sides a = 3, b = 14 and c = 12 cm. Find angle A (opposite a) to 1 decimal place. → 9.9Prompt: cos A = (b² + c² − a²)/(2bc).
- A triangle has sides 10 cm, 11 cm and 5 cm. Find its largest angle to 1 decimal place. → 87.7Prompt: The largest angle is opposite the longest side.
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 = 8, b = 7 and c = 8 cm. Find angle A (opposite a) to 1 decimal place. → 64.1Prompt: cos A = (b² + c² − a²)/(2bc).
- A triangle has sides 10 cm, 13 cm and 7 cm. Find its largest angle to 1 decimal place. → 98.2Prompt: The largest angle is opposite the longest side.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Find a side with the cosine rule.
- 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
- 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