GCSE · Pythagoras & right-angled trigonometry

Exact trig values (sin, cos and tan of 0°, 30°, 45°, 60° and 90°)Exam-style questions

Where the exact values of sin, cos and tan come from: two triangles you can sketch in seconds, half a square and half an equilateral triangle, plus a ladder lying flat or standing upright for 0° and 90°. How to use them to find an exact side in surd form, how to get an angle back from an exact ratio, and how to answer a non-calculator "show that" with exact values.

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20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    The diagram shows a right-angled triangle.x18 cm60°Diagram NOT accurately drawn

    Work out the value of xx.

    (2 marks)
    Level 2 · 2 marksTry it
  2. 2
    The diagram shows a right-angled triangle.x16 cm45°Not to scale

    Work out the exact length of xx.

    (2 marks)
    Level 2 · 2 marksTry it
  3. 3
    A straight slide in a playground is 4.84.8 m long.

    The top of the slide is 2.42.4 m above the level ground.

    The bottom of the slide is on the ground.

    Work out the angle the slide makes with the ground.

    (2 marks)
    Level 2 · 2 marksTry it