6.8 Knowledge and use of 30°, 60°, 90° triangles and 45°, 45°, 90° triangles Quiz: AQA Further Maths, Unit 6

The 20 questions

1. In a 30°, 60°, 90° triangle, the side opposite 30° is 1. What is the hypotenuse?

   • 2
   • √2
   • 3
   • √3

2. In a 30°, 60°, 90° triangle, which side is the longest?

   • Opposite the 30° angle
   • Opposite the 60° angle
   • Adjacent to 90° angle
   • Opposite the 90° angle

3. In a 45°, 45°, 90° triangle, what is the sum of the two angles other than 90°?

   • 180°
   • 45°
   • 135°
   • 90°

4. What is the ratio of the sides in a 45°, 45°, 90° triangle, listed as the two legs then the hypotenuse?

   • 1 : 1 : √2
   • 1 : 2 : 3
   • 1 : √2 : 2
   • 1 : √3 : 2

5. In a 30°, 60°, 90° triangle, what is the ratio of the sides opposite 30°, 60° and 90°?

   • 1 : √3 : 2
   • 1 : 1 : √2
   • 1 : √2 : 2
   • 1 : 2 : 3

6. What is the exact value of sin 60°?

   • √2/2
   • 1
   • 1/2
   • √3/2

7. What is the exact value of tan 60°?

   • 1/√3
   • √3
   • 2
   • 1

8. What is the exact value of sin 45°?

   • 1/2
   • √3/2
   • √2/2
   • 1

9. A ladder of length 8 m leans against a wall at 60° to the ground. What is its height on the wall, in exact form and approximately?

   • 4 m
   • 8√3 m
   • 4√2 m (about 5.66 m)
   • 4√3 m (about 6.93 m)

10. An isosceles right triangle has legs of 5 cm. What is the hypotenuse, in exact form and approximately?

    • 2.5√2 cm (about 3.54 cm)
    • 10 cm
    • 5√2 cm (about 7.07 cm)
    • 5√3 cm (about 8.66 cm)

11. A 30°, 60°, 90° triangle has hypotenuse 10 cm. What is the length of the side opposite 30°?

    • 3 cm
    • 5 cm
    • 5√3 cm
    • 10√3 cm

12. A square has side 6 cm. What is its diagonal?

    • 6√2 cm
    • 6√3 cm
    • 3√2 cm
    • 12 cm

13. What is the exact value of 2 sin 30° + cos 60°?

    • 1
    • 3/2
    • 2
    • √3

14. An equilateral triangle has side 4 cm. What is its height, in exact form?

    • √3 cm
    • 4√3 cm
    • 2√2 cm
    • 2√3 cm

15. A right-angled triangle has a 60° angle and hypotenuse 12 cm. What is the side adjacent to the 60° angle?

    • 6 cm
    • 12√3 cm
    • 6√3 cm
    • 3 cm

16. A 30°, 60°, 90° triangle has the side opposite 30° equal to 3 cm. What is the side opposite 60°?

    • 3√3 cm (about 5.20 cm)
    • 6 cm
    • 3√2 cm (about 4.24 cm)
    • 3 cm

17. What is the exact value of tan 30° × tan 60°?

    • 1/√3
    • √3
    • 1
    • 3

18. What is the exact value of sin 60° cos 30° − cos 60° sin 30°?

    • 1
    • 1/2
    • 0
    • √3/2

19. A rhombus has side 6 cm and one angle of 120°. What is its longer diagonal, in exact form?

    • 6√2 cm (about 8.49 cm)
    • 6√3 cm (about 10.39 cm)
    • 6 cm
    • 12 cm

20. A triangle has sides 1 cm, 1 cm and √2 cm. What are its angles?

    • 45°, 60° and 75°
    • 30°, 60° and 90°
    • 60°, 60° and 60°
    • 90°, 45° and 45°

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