• 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.

1. Two sides of a triangle are 3 cm and 13 cm with an angle of 97° between them. Find the area to 1 decimal place. → 19.4Prompt: Area = ½ab sin C, where C is the angle between a and b.
2. Two sides of a triangle are 13 cm and 11 cm with an angle of 116° between them. Find the area to 1 decimal place. → 64.3Prompt: Area = ½ab sin C, where C is the angle between a and b.
3. Two sides of a triangle are 9 cm and 17 cm with an angle of 149° between them. Find the area to 1 decimal place. → 39.4Prompt: Area = ½ab sin C, where C is the angle between a and b.

• 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.

• 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.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. A triangle has area 35.7 cm², one side of 6 cm and an included angle of 132°. Find the other side next to that angle, to the nearest cm. → 16Prompt: Area = ½ab sin C. Substitute what you know.
2. A triangle has sides 9 cm and 11 cm with an acute angle θ between them. Its area is 40 cm². Find θ to 1 decimal place. → 53.9Prompt: Rearrange: sin θ = 2 × area ÷ (ab).

• 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 6 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. A triangle has area 74.7 cm², one side of 13 cm and an included angle of 130°. Find the other side next to that angle, to the nearest cm. → 15Prompt: Area = ½ab sin C. Substitute what you know.
2. A triangle has sides 14 cm and 16 cm with an acute angle θ between them. Its area is 80.6 cm². Find θ to 1 decimal place. → 46Prompt: Rearrange: sin θ = 2 × area ÷ (ab).

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.