Lesson G20

G20 Pythagoras' theorem and trigonometry in right-angled triangles Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G20, Pythagoras' theorem and trigonometry in right-angled triangles: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. State Pythagoras' theorem for a right-angled triangle with shorter sides a and b and hypotenuse c.

    • a^2 + b^2 = 2c
    • a + b = c
    • a^2 + b^2 = c^2
    • a^2 - b^2 = c^2

  2. In a right-angled triangle, which side is the hypotenuse?

    • The side opposite the smallest angle
    • The shortest side
    • The side opposite the right angle
    • The side adjacent to angle theta

  3. Which ratio is sin theta in a right-angled triangle?

    • opposite / hypotenuse
    • adjacent / hypotenuse
    • opposite / adjacent
    • hypotenuse / opposite

  4. Which ratio is tan theta in a right-angled triangle?

    • opposite / hypotenuse
    • opposite / adjacent
    • adjacent / hypotenuse
    • adjacent / opposite

  5. Which ratio is cos theta in a right-angled triangle?

    • adjacent / hypotenuse
    • hypotenuse / adjacent
    • opposite / hypotenuse
    • adjacent / opposite

  6. A right-angled triangle has shorter sides 3 cm and 4 cm. What is the length of the hypotenuse?

    • 25 cm
    • 5 cm
    • 7 cm
    • 12 cm

  7. Which expression gives a shorter side a, given hypotenuse c and other shorter side b?

    • a = c^2 + b^2
    • a = sqrt(c^2 - b^2)
    • a = c^2 - b^2
    • a = sqrt(c^2 + b^2)

  8. A right-angled triangle has an angle theta with sin theta = 0.6 and hypotenuse 5 cm. What is the length of the opposite side?

    • 3 cm
    • 0.6 cm
    • 4 cm
    • 5.6 cm

  9. A right-angled triangle has shorter sides 5 cm and 12 cm. What is the length of the hypotenuse?

    • 119 cm
    • 7 cm
    • 13 cm
    • 17 cm

  10. A 6.5 m ladder leans against a wall with its foot 2.5 m from the wall. How high up the wall does it reach?

    • 8.5 m
    • 4.0 m
    • 6.0 m
    • 9.0 m

  11. In a right-angled triangle the opposite side is 7 cm and the adjacent side is 10 cm. Find the angle theta to 1 decimal place.

    • 20.6 degrees
    • 55.0 degrees
    • 35.0 degrees
    • 70.0 degrees

  12. In a right-angled triangle the opposite side is 8 cm and the hypotenuse is 12 cm. Find the angle theta to 1 decimal place.

    • 41.8 degrees
    • 48.2 degrees
    • 56.3 degrees
    • 33.7 degrees

  13. A right-angled triangle has adjacent side 9 cm and angle theta = 32 degrees. Find the hypotenuse to 1 decimal place.

    • 10.6 cm
    • 7.6 cm
    • 4.8 cm
    • 15.4 cm

  14. A right-angled triangle has opposite side 5 cm and angle theta = 50 degrees. Find the adjacent side to 2 decimal places.

    • 2.98 cm
    • 6.42 cm
    • 4.20 cm
    • 3.83 cm

  15. A kite is flown on a 50 m string held at 40 degrees to the horizontal, with the string taut from the ground. What is the height of the kite to the nearest metre?

    • 32 m
    • 38 m
    • 25 m
    • 43 m

  16. A right-angled triangle has sides 5, 12 and 13. What is cos theta for the angle opposite the side of length 5?

    • 5/12
    • 12/5
    • 5/13
    • 12/13

  17. (H) A cuboid measures 3 cm by 4 cm by 12 cm. What is the length of its space diagonal?

    • 15 cm
    • 19 cm
    • 13 cm
    • 12.6 cm

  18. (H) A square-based pyramid has base side 6 cm and vertical height 4 cm. What is the distance from the apex to the midpoint of a base edge?

    • 2 cm
    • 5 cm
    • 4 cm
    • 7.2 cm

  19. (H) A rectangle has sides 6 cm and 8 cm. What is the length of its diagonal?

    • 10 cm
    • 14 cm
    • 2 cm
    • 48 cm

  20. (H) A line of length 20 cm makes an angle of 30 degrees with the horizontal. What is its vertical height?

    • 17.3 cm
    • 20 cm
    • 34.6 cm
    • 10 cm

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