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Math lesson plan · 11th grade (Year 12 in England) · 45 minutes

Decide which rule solves a triangle

Trigonometry

CCSS HSG.SRT.D.10CCSS HSG.SRT.D.11England: GCSE Higher Geometry

Objective and success criteria

Students will: Decide which rule solves a triangle.

  • 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 a side with the sine rule; Find a side with the cosine rule

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 (Find a side with the sine rule; Find a side with the cosine rule). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. In triangle ABC, A = 74°, B = 58° and a = 14 cm. Find b to 1 decimal place. → 12.4Prompt: a/sin A = b/sin B.
  2. In triangle ABC, b = 6 cm, c = 13 cm and A = 88°. Find a to 1 decimal place. → 14.1Prompt: a² = b² + c² − 2bc cos A.
  3. In triangle ABC, A = 40°, C = 84° and a = 6 cm. Find b to 1 decimal place. → 7.7Prompt: You need angle B, opposite b. Use the angle sum first.

Hook · 5 min

  • Show a ramp or a ladder against a wall and ask how steep it is.
  • Share the objective: Decide which rule solves a triangle. 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: You know two sides and an angle opposite one of them; find another angle. Which is the most direct method?
  • Step 1: Sine rule
  • Answer: Sine rule
  • 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.
  1. You know two angles and a side; find another side. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Sine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.
  2. You know two sides and an angle opposite one of them; find another angle. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Sine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.

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 6 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.
  1. You know a right angle, one other angle and the hypotenuse; find a shorter side. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → SOH CAH TOA (right angle)Prompt: Is there a right angle? If so, basic trigonometry is enough.
  2. You know two sides and an angle opposite one of them; find another angle. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Sine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.

Watch out for

  • Mixing up opposite and adjacent sides.
  • Calculator in radians instead of degrees.

Support and stretch

Support

  • Review first: Find a side with the sine rule.
  • 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

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Decide which rule solves a triangle

Name

Date

Score/ 6

  1. Question 1

    You know a right angle, one other angle and the hypotenuse; find a shorter side. Which is the most direct method?

    • A. Sine rule
    • B. Cosine rule
    • C. SOH CAH TOA (right angle)

  2. Question 2

    You know two angles and the side between them; find a side opposite one of them. Which is the most direct method?

    • A. Sine rule
    • B. Cosine rule
    • C. SOH CAH TOA (right angle)

  3. Question 3

    You know all three sides; find an angle. Which is the most direct method?

    • A. Sine rule
    • B. Cosine rule
    • C. SOH CAH TOA (right angle)

  4. Question 4

    You know two sides and the angle between them; find the third side. Which is the most direct method?

    • A. Sine rule
    • B. Cosine rule
    • C. SOH CAH TOA (right angle)

  5. Question 5

    You know two angles and a side; find another side. Which is the most direct method?

    • A. Sine rule
    • B. Cosine rule
    • C. SOH CAH TOA (right angle)

  6. Question 6

    You know two sides and an angle opposite one of them; find another angle. Which is the most direct method?

    • A. Sine rule
    • B. Cosine rule
    • C. SOH CAH TOA (right angle)

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Answer key: Decide which rule solves a triangle

  1. 1. C. SOH CAH TOA (right angle)

  2. 2. A. Sine rule

  3. 3. B. Cosine rule

  4. 4. B. Cosine rule

  5. 5. A. Sine rule

  6. 6. A. Sine rule