ChalkHour

Year 10 Maths: Trigonometry lesson pack

A complete, ready-to-teach GCSE lesson on trigonometry. Below is a real sample of what ChalkHour makes: the full pack adds three levels of worksheet, model answers, a teaching explainer and print-ready PDF and Word files.

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Real sample

Introduction to Right-Angled Trigonometry

This lesson introduces the three primary trigonometric ratios (sin, cos, tan) to find missing sides and angles in right-angled triangles. It builds on previous knowledge of Pythagoras' Theorem and ratio.

Learning objectives

  • Identify the hypotenuse, opposite, and adjacent sides of a right-angled triangle relative to a given angle.
  • Calculate missing side lengths in right-angled triangles using sine, cosine, and tangent ratios.
  • Calculate missing angles in right-angled triangles using inverse trigonometric functions.
  • Solve multi-step problems involving trigonometry in context.

Lesson plan (60 minutes)

  1. Introduction · 10 min

    Starter: Recall Pythagoras' Theorem and identifying sides of a right-angled triangle (Hypotenuse).

  2. Teaching · 15 min

    Direct Instruction: Introduction of SOH CAH TOA, labelling Opposite/Adjacent, and the step-by-step method for finding sides.

  3. Guided Practice · 10 min

    Guided Practice: Working through a 'finding an angle' example together using inverse functions.

  4. Independent Practice · 20 min

    Independent Practice: Differentiated worksheets (Support, Core, Stretch).

  5. Assessment · 5 min

    Plenary: Multiple-choice quiz to check for understanding and address misconceptions.

Key vocabulary

Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Opposite
The side across from the specific angle being used.
Adjacent
The side next to the specific angle being used, which is not the hypotenuse.
Trigonometric Ratio
A number expressing the relationship between two sides of a triangle.
Inverse Function
The function used to find an angle when the sides are known (e.g., sin⁻¹).

Core worksheet (first questions)

  1. A ladder 12m long leans against a wall at an angle of 60° to the ground. How high up the wall does it reach?
  2. A triangle has an opposite side of 9cm and an adjacent side of 8cm. Find the angle θ.
  3. Find x if the angle is 40°, the opposite side is 10cm and x is the adjacent side.
  4. Calculate the height of a triangle with a hypotenuse of 9.8cm and a base angle of 35°.

Quiz (sample)

  1. 1. What is the common mnemonic used to remember the trig ratios?

    • A. SOH CAH TOA
    • B. SAH COH TOA
    • C. SOH CIH TUA
    • D. SOA CAH TOH

  2. 2. What is the ratio for Sine (sin)?

    • A. Adjacent / Hypotenuse
    • B. Opposite / Adjacent
    • C. Opposite / Hypotenuse
    • D. Hypotenuse / Opposite

  3. 3. What is the ratio for Cosine (cos)?

    • A. Opposite / Hypotenuse
    • B. Adjacent / Hypotenuse
    • C. Opposite / Adjacent
    • D. Hypotenuse / Adjacent

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Support and Stretch worksheets, every answer and model answer, the teaching explainer and common misconceptions, editable and ready to print as PDF or Word.

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