Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Find a side with the sine rule
Trigonometry
CCSS HSG.SRT.D.11England: GCSE Higher Geometry
Objective and success criteria
Students will: Find a side with the sine 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: The sine rule (law of sines)
Leads to: Find an angle with the sine rule; Decide which rule solves a triangle
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 (The sine rule (law of sines)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- In triangle ABC, angle A = 80°, angle B = 61° and side a = 20 cm. Find side b to 1 decimal place. → 17.8Prompt: Sine rule: a/sin A = b/sin B.
- In triangle ABC, a = 17 cm, b = 9 cm and angle A = 48°. Find angle B (acute) to 1 decimal place. → 23.2Prompt: Sine rule for angles: sin B / b = sin A / a.
- In triangle ABC, angle A = 49°, angle B = 40° and side a = 8 cm. Find side b to 1 decimal place. → 6.8Prompt: Sine rule: a/sin A = b/sin B.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Find a side with the sine 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: In triangle ABC, A = 47°, B = 46° and a = 17 cm. Find b to 1 decimal place.
- Step 1: b = 17 × sin 46° ÷ sin 47°
- Step 2: b ≈ 16.7 cm
- Answer: 16.7
- 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.
- In triangle ABC, A = 53°, B = 70° and a = 19 cm. Find b to 1 decimal place. → 22.4Prompt: a/sin A = b/sin B.
- In triangle ABC, A = 36°, C = 93° and a = 5 cm. Find b to 1 decimal place. → 6.6Prompt: You need angle B, opposite b. Use the angle sum first.
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.
- Two surveyors stand at P and Q, 70 m apart on one bank of a river. A tree R is on the other bank. Angle RPQ = 35° and angle PQR = 90°. How far is the tree from Q? Give 1 decimal place. → 49Prompt: Find the angle at R first.
- In triangle ABC, A = 65°, B = 64° and a = 8 cm. Find b to 1 decimal place. → 7.9Prompt: a/sin A = b/sin B.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: The sine rule (law of sines).
- 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 an angle with the sine rule; Decide which rule solves a triangle.
- 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