Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Area of a triangle: ½ab sin C
Trigonometry
CCSS HSG.SRT.D.9England: GCSE Higher Geometry
Objective and success criteria
Students will: Area of a triangle: ½ab sin C.
- 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; Area of triangles
Leads to: Use ½ab sin C to find a side or an angle; Find the area of a circular segment
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; Area of triangles). 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: Area of a triangle: ½ab sin C. 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: Two sides of a triangle are 18 cm and 10 cm with an angle of 149° between them. Find the area to 1 decimal place.
- Step 1: ½ × 18 × 10 × sin 149° ≈ 46.4 cm²
- Answer: 46.4
- 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.
- Two sides of a triangle are 10 cm and 13 cm with an angle of 111° between them. Find the area to 1 decimal place. → 60.7Prompt: Area = ½ab sin C, where C is the angle between a and b.
- Two sides of a triangle are 16 cm and 8 cm with an angle of 62° between them. Find the area to 1 decimal place. → 56.5Prompt: Area = ½ab sin C, where C is the angle between a and b.
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 sides of a triangle are 17 cm and 20 cm with an angle of 20° between them. Find the area to 1 decimal place. → 58.1Prompt: Area = ½ab sin C, where C is the angle between a and b.
- Two sides of a triangle are 20 cm and 7 cm with an angle of 84° between them. Find the area to 1 decimal place. → 69.6Prompt: Area = ½ab sin C, where C is the angle between a and b.
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: Use ½ab sin C to find a side or an angle; Find the area of a circular segment.
- 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