Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Use ½ab sin C to find a side or an angle
Trigonometry
CCSS HSG.SRT.D.9England: GCSE Higher Geometry
Objective and success criteria
Students will: Use ½ab sin C to find a side or an angle.
- 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: Area of a triangle: ½ab sin C
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 (Area of a triangle: ½ab sin C). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Two sides of a triangle are 19 cm and 18 cm with an angle of 118° between them. Find the area to 1 decimal place. → 151Prompt: Area = ½ab sin C, where C is the angle between a and b.
- Two sides of a triangle are 18 cm and 11 cm with an angle of 75° between them. Find the area to 1 decimal place. → 95.6Prompt: Area = ½ab sin C, where C is the angle between a and b.
- Two sides of a triangle are 18 cm and 9 cm with an angle of 105° between them. Find the area to 1 decimal place. → 78.2Prompt: Area = ½ab sin C, where C is the angle between a and b.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Use ½ab sin C to find a side or an angle. 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 area 14.1 cm², one side of 8 cm and an included angle of 118°. Find the other side next to that angle, to the nearest cm.
- Step 1: b = 2 × 14.1 ÷ (8 × sin 118°) ≈ 3.99
- Step 2: ≈ 4 cm
- Answer: 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.
- A triangle has area 28.3 cm², one side of 10 cm and an included angle of 54°. Find the other side next to that angle, to the nearest cm. → 7Prompt: Area = ½ab sin C. Substitute what you know.
- A triangle has sides 15 cm and 13 cm with an acute angle θ between them. Its area is 93.2 cm². Find θ to 1 decimal place. → 72.9Prompt: Rearrange: sin θ = 2 × area ÷ (ab).
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 area 56.7 cm², one side of 8 cm and an included angle of 71°. Find the other side next to that angle, to the nearest cm. → 15Prompt: Area = ½ab sin C. Substitute what you know.
- A triangle has sides 6 cm and 7 cm with an acute angle θ between them. Its area is 20.7 cm². Find θ to 1 decimal place. → 80.3Prompt: Rearrange: sin θ = 2 × area ÷ (ab).
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Area of a triangle: ½ab sin C.
- 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