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

Choose sine, cosine or tangent for a problem

Trigonometry

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

Objective and success criteria

Students will: Choose sine, cosine or tangent for a problem.

  • 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: Label hypotenuse, opposite and adjacent sides

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 · 6 min

  • Quick retrieval from earlier learning (Label hypotenuse, opposite and adjacent sides). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. In triangle XZR, the right angle is at Z. Using angle X, which side is the opposite? (ZR / XZ / XR) → ZRPrompt: Sketch the triangle and mark the right angle.
  2. In triangle YXM, the right angle is at X. Using angle Y, which side is the hypotenuse? (YX / YM / XM) → YMPrompt: Sketch the triangle and mark the right angle.
  3. In triangle ZMN, the right angle is at M. Using angle Z, which side is the adjacent? (ZM / MN / ZN) → ZMPrompt: Sketch the triangle and mark the right angle.

Hook · 6 min

  • Show a ramp or a ladder against a wall and ask how steep it is.
  • Share the objective: Choose sine, cosine or tangent for a problem. 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: In a right triangle you know angle θ and the hypotenuse. You want the adjacent side. Which ratio should you use?
  • Step 1: cos
  • Answer: cos
  • 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. In a right triangle you know angle θ and the hypotenuse. You want the opposite side. Which ratio should you use? (sin / cos / tan) → sinPrompt: SOH CAH TOA: which ratio links the two sides involved?
  2. A 15 m ladder leans against a wall at 29° to the ground. To find how high up the wall it reaches, which ratio do you use with the 29° angle? (sin / cos / tan) → sinPrompt: The ladder is the hypotenuse.

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. In a right triangle you know angle θ and the opposite side. You want the hypotenuse. Which ratio should you use? (sin / cos / tan) → sinPrompt: SOH CAH TOA: which ratio links the two sides involved?
  2. A 5 m ladder leans against a wall at 54° to the ground. To find how high up the wall it reaches, which ratio do you use with the 54° angle? (sin / cos / tan) → sinPrompt: The ladder is the hypotenuse.

Watch out for

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

Support and stretch

Support

  • Review first: Label hypotenuse, opposite and adjacent sides.
  • 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-10.

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

eurekami

Choose sine, cosine or tangent for a problem

Name

Date

Score/ 8

  1. Question 1

    A 16 m ladder leans against a wall at 36° to the ground. To find how high up the wall it reaches, which ratio do you use with the 36° angle?

    • A. sin
    • B. cos
    • C. tan

  2. Question 2

    In a right triangle you know angle θ and the hypotenuse. You want the opposite side. Which ratio should you use?

    • A. sin
    • B. cos
    • C. tan

  3. Question 3

    A 16 m ladder leans against a wall at 42° to the ground. To find how high up the wall it reaches, which ratio do you use with the 42° angle?

    • A. sin
    • B. cos
    • C. tan

  4. Question 4

    In a right triangle you know angle θ and the opposite side. You want the adjacent side. Which ratio should you use?

    • A. sin
    • B. cos
    • C. tan

  5. Question 5

    A 10 m ladder leans against a wall at 33° to the ground. To find how high up the wall it reaches, which ratio do you use with the 33° angle?

    • A. sin
    • B. cos
    • C. tan

  6. Question 6

    In a right triangle you know angle θ and the opposite side. You want the hypotenuse. Which ratio should you use?

    • A. sin
    • B. cos
    • C. tan

  7. Question 7

    A 20 m ladder leans against a wall at 31° to the ground. To find how high up the wall it reaches, which ratio do you use with the 31° angle?

    • A. sin
    • B. cos
    • C. tan

  8. Question 8

    A 16 m ladder leans against a wall at 24° to the ground. To find how high up the wall it reaches, which ratio do you use with the 24° angle?

    • A. sin
    • B. cos
    • C. tan

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Answer key: Choose sine, cosine or tangent for a problem

  1. 1. A. sin

  2. 2. A. sin

  3. 3. A. sin

  4. 4. C. tan

  5. 5. A. sin

  6. 6. A. sin

  7. 7. A. sin

  8. 8. A. sin