Lesson T4.6.2

T4.6.2 Trigonometric ratios in right-angled triangles Quiz: KS3 Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson T4.6.2, Trigonometric ratios in right-angled triangles: 20 multiple choice questions for the KS3 Maths (National Curriculum), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. In trigonometry, what does SOH mean for sine?

    • Sine equals adjacent over hypotenuse
    • Sine equals hypotenuse over opposite
    • Sine equals opposite over adjacent
    • Sine equals opposite over hypotenuse

  2. What is cos θ equal to in a right-angled triangle?

    • Adjacent over opposite
    • Opposite over hypotenuse
    • Opposite over adjacent
    • Adjacent over hypotenuse

  3. What is tan θ equal to?

    • Hypotenuse over opposite
    • Opposite over adjacent
    • Opposite over hypotenuse
    • Adjacent over opposite

  4. Which side is the hypotenuse in a right-angled triangle?

    • The shortest side
    • The base of the triangle
    • The side opposite the right angle
    • The side next to the angle θ

  5. In a right-angled triangle with angle θ, the opposite side is 5 cm and the hypotenuse is 10 cm. What is sin θ?

    • 2
    • 0.2
    • 0.5
    • 0.25

  6. A right-angled triangle has hypotenuse 10 cm and an angle of 40 degrees. What is the length of the opposite side, to 1 decimal place?

    • 4.2 cm
    • 15.6 cm
    • 6.4 cm
    • 7.7 cm

  7. A right-angled triangle has adjacent side 8 cm and angle 60 degrees. What is the opposite side, to 1 decimal place?

    • 13.9 cm
    • 6.9 cm
    • 16.0 cm
    • 4.0 cm

  8. Which angle has a sine of 0.5?

    • 60 degrees
    • 45 degrees
    • 30 degrees
    • 90 degrees

  9. What is cos 60 degrees?

    • 0.866
    • 0
    • 1
    • 0.5

  10. A ramp is 10 m long and rises 2 m. What angle does it make with the ground, to 1 decimal place?

    • 11.5 degrees
    • 2 degrees
    • 78.5 degrees
    • 20 degrees

  11. A right-angled triangle has hypotenuse 12 cm and angle 35 degrees. What is the adjacent side, to 1 decimal place?

    • 9.8 cm
    • 6.9 cm
    • 8.1 cm
    • 14.6 cm

  12. A person stands 40 m from the base of a tower. The angle of elevation to the top is 30 degrees. How tall is the tower, to 1 decimal place?

    • 23.1 m
    • 34.6 m
    • 40 m
    • 69.3 m

  13. A ladder 6 m long leans at 70 degrees to the ground. How high up the wall does it reach, to 1 decimal place?

    • 5.6 m
    • 4.8 m
    • 6.9 m
    • 2.1 m

  14. You know the opposite and adjacent sides of a right-angled triangle. Which ratio should you use to find the angle?

    • Cosine
    • Sine
    • Pythagoras only
    • Tangent

  15. In a right-angled triangle, sin A = 3/5 and the hypotenuse is 15 cm. What is the length of the side opposite A?

    • 9 cm
    • 12 cm
    • 3 cm
    • 5 cm

  16. tan θ = 2.5. What is θ to 1 decimal place?

    • 68.2 degrees
    • 21.8 degrees
    • 2.5 degrees
    • 45 degrees

  17. A right-angled triangle has hypotenuse 13 cm and angle 22.6 degrees. What is the opposite side, to 1 decimal place?

    • 7.6 cm
    • 4.8 cm
    • 5.0 cm
    • 12.0 cm

  18. A kite string of length 30 m makes an angle of 50 degrees with the ground. How high is the kite above the ground, to 1 decimal place?

    • 19.3 m
    • 46.0 m
    • 23.0 m
    • 30.0 m

  19. Which value equals sin 60 degrees?

    • cos 30 degrees
    • cos 60 degrees
    • cos 120 degrees
    • cos 90 degrees

  20. What is tan 45 degrees?

    • 0
    • 1.414
    • 0.707
    • 1

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