Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
The sine rule (law of sines)
Trigonometry
CCSS HSG.SRT.D.10CCSS HSG.SRT.D.11England: GCSE Higher Geometry
Objective and success criteria
Students will: The sine rule (law of sines).
- 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 angles with inverse trig; Classify triangles; angles in a triangle
Leads to: Find a side with the sine 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 (Find angles with inverse trig; Classify triangles; angles in a triangle). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A right triangle has opposite side 12 cm and adjacent side 8 cm to angle θ. Find θ to 1 decimal place. → 56.3Prompt: Opposite and adjacent: use tan.
- In a right triangle the hypotenuse is 8 m and the side opposite angle θ is 4 m. Find θ to 1 decimal place. → 30Prompt: Opposite and hypotenuse: use sin.
- A right triangle has opposite side 3 cm and adjacent side 11 cm to angle θ. Find θ to 1 decimal place. → 15.3Prompt: Opposite and adjacent: use tan.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: The sine rule (law of sines). 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, angle A = 44°, angle B = 73° and side a = 14 cm. Find side b to 1 decimal place.
- Step 1: b = 14 × sin 73° / sin 44°
- Step 2: ≈ 19.3 cm
- Answer: 19.3
- 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, angle A = 54°, angle B = 30° and side a = 10 cm. Find side b to 1 decimal place. → 6.2Prompt: Sine rule: a/sin A = b/sin B.
- In triangle ABC, a = 19 cm, b = 4 cm and angle A = 52°. Find angle B (acute) to 1 decimal place. → 9.5Prompt: Sine rule for angles: sin B / b = sin A / a.
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.
- In triangle ABC, angle A = 46°, angle B = 69° and side a = 5 cm. Find side b to 1 decimal place. → 6.5Prompt: Sine rule: a/sin A = b/sin B.
- In triangle ABC, a = 16 cm, b = 4 cm and angle A = 74°. Find angle B (acute) to 1 decimal place. → 13.9Prompt: Sine rule for angles: sin B / b = sin A / a.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Find angles with inverse trig.
- 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 sine 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