6.5 Be able to apply trigonometry and Pythagoras’ theorem to 2 and 3 dimensional problems Quiz: AQA Further Maths, Unit 6

The 20 questions

1. Which ratio is used to find an angle when the opposite and adjacent sides of a right-angled triangle are known?

   • Tangent
   • Cosine
   • Cosecant
   • Sine

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

   • The base
   • The adjacent side
   • The hypotenuse
   • The shorter leg

3. What is used with the line itself to measure the angle between a line and a plane?

   • The normal vector
   • Its projection
   • The intersecting vertex
   • An adjacent edge

4. Which type of lines in each plane are used to measure the angle between two intersecting planes?

   • Bisecting lines
   • Parallel lines
   • Perpendicular lines
   • Diagonal lines

5. In the sine rule, what is each side of a triangle divided by?

   • Sine of opposite angle
   • Sine of adjacent angle
   • Cosine of opposite angle
   • Hypotenuse length

6. Which formula gives the area of a triangle from two sides a and b and the angle C between them?

   • Area = ½ab cos C
   • Area = ab sin C
   • Area = ½(a + b) sin C
   • Area = ½ab sin C

7. In a right-angled triangle, tan θ equals which ratio?

   • Opposite ÷ hypotenuse
   • Opposite ÷ adjacent
   • Adjacent ÷ opposite
   • Hypotenuse ÷ adjacent

8. In a right-angled triangle, cos θ equals which ratio?

   • Opposite ÷ hypotenuse
   • Adjacent ÷ opposite
   • Adjacent ÷ hypotenuse
   • Hypotenuse ÷ adjacent

9. A 6 m ladder makes an angle of 70° with the ground. How high up a wall does it reach, to 1 decimal place?

   • 2.1 m
   • 6.4 m
   • 5.1 m
   • 5.6 m

10. A ramp rises 1.5 m over a horizontal distance of 8 m. What angle does it make with the horizontal, to 1 decimal place?

    • 18.6°
    • 79.4°
    • 10.6°
    • 7.1°

11. From a point 20 m from the base of a tree, the angle of elevation of the top is 35°. What is the tree's height, to 1 decimal place?

    • 11.5 m
    • 28.6 m
    • 16.4 m
    • 14.0 m

12. The top of a 30 m cliff has an angle of depression of 25° to a boat. To the nearest metre, how far is the boat from the foot of the cliff?

    • 69 m
    • 64 m
    • 13 m
    • 29 m

13. A vertical pole OT is 4 m tall. P is on level ground 3 m from O. What is the angle of elevation of T from P, to 1 decimal place?

    • 36.9°
    • 67.4°
    • 48.0°
    • 53.1°

14. Triangle ABC has angle A = 40°, angle B = 70° and side a = 8 cm. Using the sine rule, what is side b, to 1 decimal place?

    • 5.5 cm
    • 13.9 cm
    • 11.7 cm
    • 9.3 cm

15. A triangle has sides 7 cm and 9 cm enclosing an angle of 60°. What is the third side, to 2 decimal places?

    • 9.00 cm
    • 11.40 cm
    • 7.00 cm
    • 8.19 cm

16. A line AB has end A on a horizontal plane and end B 3 m above it. The horizontal projection of AB is 4 m. What is the angle between AB and the plane, to 1 decimal place?

    • 53.1°
    • 30.0°
    • 36.9°
    • 48.6°

17. A cuboid is 3 cm by 4 cm by 12 cm. What is the angle between its space diagonal and its base, to 1 decimal place?

    • 67.4°
    • 36.9°
    • 22.6°
    • 53.1°

18. A square pyramid has a base of side 6 cm, and its apex is 4 cm vertically above the centre. What is the angle between a sloping edge and the base, to 1 decimal place?

    • 56.3°
    • 35.3°
    • 47.7°
    • 43.3°

19. In triangle ABC, a = 5 cm, b = 8 cm and angle A = 30°. How many different triangles satisfy these conditions?

    • None
    • Two
    • One
    • Infinitely many

20. Triangle PQR has PQ = 7 cm, PR = 9 cm and angle Q = 40°. What is angle R, to 1 decimal place?

    • 30.0°
    • 50.0°
    • 150.0°
    • 40.0°

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