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Math lesson plan · 10th grade (Year 11 in England) · 60 minutes

Trigonometric ratios: SOH CAH TOA

Trigonometry

CCSS HSG.SRT.C.6CCSS HSG.SRT.C.8England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Objective and success criteria

Students will: Trigonometric ratios: SOH CAH TOA.

  • 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: Pythagoras' theorem; Similar shapes

Leads to: Pythagoras and trigonometry in 3D; Find angles with inverse trig; Exact trig values (0°, 30°, 45°, 60°, 90°)

Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Pythagoras' theorem; Similar shapes). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Triangles ABC and DEF are similar. AB = 6 cm, BC = 11 cm and DE = 9 cm. Find EF in cm. → 16.5Prompt: Find the scale factor from the matching sides AB and DE.
  2. Triangles ABC and DEF are similar. AB = 7 cm, BC = 12 cm and DE = 17.5 cm. Find EF in cm. → 30Prompt: Find the scale factor from the matching sides AB and DE.
  3. Triangles ABC and DEF are similar. AB = 7 cm, BC = 6 cm and DE = 14 cm. Find EF in cm. → 12Prompt: Find the scale factor from the matching sides AB and DE.

Hook · 6 min

  • Show a ramp or a ladder against a wall and ask how steep it is.
  • Share the objective: Trigonometric ratios: SOH CAH TOA. Read the success criteria together.

I do: model it · 12 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A ramp rises at 64° over a horizontal distance of 10 m. How high does it rise? Give 1 decimal place.
  • Step 1: 10 × tan 64° = 20.503
  • Step 2: ≈ 20.5 m
  • Answer: 20.5
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 12 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. A ramp rises at 23° over a horizontal distance of 18 m. How high does it rise? Give 1 decimal place. → 7.6Prompt: You know the adjacent side and want the opposite: use tan.
  2. A ramp rises at 55° over a horizontal distance of 16 m. How high does it rise? Give 1 decimal place. → 22.9Prompt: You know the adjacent side and want the opposite: use tan.

You do: independent practice · 17 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 · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. A ramp rises at 56° over a horizontal distance of 4 m. How high does it rise? Give 1 decimal place. → 5.9Prompt: You know the adjacent side and want the opposite: use tan.
  2. A ramp rises at 32° over a horizontal distance of 22 m. How high does it rise? Give 1 decimal place. → 13.7Prompt: You know the adjacent side and want the opposite: use tan.

Watch out for

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

Support and stretch

Support

  • Review first: Pythagoras' theorem.
  • 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: Pythagoras and trigonometry in 3D; Find angles with inverse trig; Exact trig values (0°, 30°, 45°, 60°, 90°).
  • 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-10.

Free lesson plan from eurekami.com/lesson-plan-builder

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Trigonometric ratios: SOH CAH TOA

Name

Date

Score/ 8

  1. Question 1

    In a right triangle, angle θ has opposite side 7, adjacent side 24 and hypotenuse 25. What is sin θ?

    24725θ
    • A. 7/25
    • B. 7/24
    • C. 25/7
    • D. 24/25

  2. Question 2

    A right triangle has hypotenuse 23 cm and an angle of 35°. Find the side adjacent to the 35° angle, to 1 decimal place.

    23 cm35°

    Answer

  3. Question 3

    A ramp rises at 73° over a horizontal distance of 22 m. How high does it rise? Give 1 decimal place.

    Answer

  4. Question 4

    In a right triangle, angle θ has opposite side 8, adjacent side 15 and hypotenuse 17. What is cos θ?

    15817θ
    • A. 8/15
    • B. 17/8
    • C. 15/17
    • D. 8/17

  5. Question 5

    A right triangle has hypotenuse 21 cm and an angle of 60°. Find the side opposite the 60° angle, to 1 decimal place.

    21 cm60°

    Answer

  6. Question 6

    A ramp rises at 58° over a horizontal distance of 25 m. How high does it rise? Give 1 decimal place.

    Answer

  7. Question 7

    In a right triangle, angle θ has opposite side 8, adjacent side 15 and hypotenuse 17. What is sin θ?

    15817θ
    • A. 15/17
    • B. 8/17
    • C. 15/8
    • D. 8/15

  8. Question 8

    A right triangle has hypotenuse 23 cm and an angle of 44°. Find the side adjacent to the 44° angle, to 1 decimal place.

    23 cm44°

    Answer

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Answer key: Trigonometric ratios: SOH CAH TOA

  1. 1. A. 7/25

  2. 2. 18.8

  3. 3. 72

  4. 4. C. 15/17

  5. 5. 18.2

  6. 6. 40

  7. 7. B. 8/17

  8. 8. 16.5