6.3 Sine and cosine rules in scalene triangles; area of a triangle = ab sinC Quiz: AQA Further Maths, Unit 6

The 20 questions

1. What is the sine rule?

   • a / sin A = b / cos B
   • a^2 = b^2 + c^2
   • a / cos A = b / cos B
   • a / sin A = b / sin B = c / sin C

2. What is the cosine rule for a^2?

   • a^2 = b^2 + c^2 + 2bc cos A
   • a^2 = b^2 - c^2
   • a^2 = b^2 + c^2 - 2bc cos A
   • a = b + c - cos A

3. What is the formula for the area of a triangle using two sides and the included angle?

   • Area = (1/2) ab tan C
   • Area = (1/2) ab sin C
   • Area = (1/2) ab cos C
   • Area = ab sin C

4. In a triangle, a = 8, A = 30 degrees and B = 45 degrees. What is b?

   • 4 sqrt(2)
   • 16
   • 12
   • 8 sqrt(2)

5. A triangle has a = 5, b = 6 and C = 60 degrees. What is c?

   • sqrt(41)
   • sqrt(61)
   • sqrt(31)
   • 11

6. A triangle has a = 6, b = 8 and C = 30 degrees. What is its area?

   • 6
   • 12
   • 24
   • 24 sqrt(3)

7. A triangle has sides a = 7, b = 8 and c = 5. What is angle A?

   • 60 degrees
   • 30 degrees
   • 120 degrees
   • 45 degrees

8. Which rule is used to find the third side when two sides and the included angle are known?

   • Circle theorem
   • Tangent ratio only
   • Sine rule
   • Cosine rule

9. Which rule is used when two angles and one side are known?

   • Pythagoras' theorem
   • Sine rule
   • Cosine rule
   • Area formula only

10. If a = 10, A = 40 degrees and B = 70 degrees, which expression gives b?

    • 10 sin 40 / sin 70
    • 10 cos 70 / cos 40
    • 10 sin 70 / sin 40
    • 10 sin 70 x sin 40

11. In any triangle, where is the largest interior angle always located?

    • Between equal sides
    • Opposite longest side
    • Opposite shortest side
    • Adjacent longest side

12. How many sides have equal length in a scalene triangle?

    • Three
    • One
    • Zero
    • Two

13. Find the area of a triangle with sides 5 and 7 and included angle 120 degrees.

    • 70 sqrt(3)
    • 35 sqrt(3) / 2
    • 35 sqrt(3) / 4
    • 35 / 4

14. A triangle has sides a = 4, b = 5 and c = 6. What is cos C?

    • 1/8
    • -1/8
    • 5/8
    • 1/4

15. Two sides of a right-angled triangle are 3 and 4, with the right angle between them. What is the third side?

    • sqrt(7)
    • 5
    • 7
    • 25

16. In a triangle with side lengths 7 cm, 8 cm, and 9 cm, which angle is largest?

    • Between 8 and 9
    • Opposite 8 cm
    • Opposite 9 cm
    • Opposite 7 cm

17. Which given set of measurements creates the ambiguous case when using the sine rule?

    • AAS
    • SAS
    • SSS
    • SSA

18. A triangle has a = 10, b = 12 and C = 30 degrees. What is its area?

    • 15
    • 60
    • 30
    • 30 sqrt(3)

19. In a triangle with a = 5, b = 7 and A = 30 degrees, which expression gives sin B?

    • 7 sin 30 / 5
    • 5 sin 30 / 7
    • 7 cos 30 / 5
    • 5 sin 30 x 7

20. A triangle has sides 5 and 5 with included angle 60 degrees. What is the third side?

    • 7
    • 5
    • 10
    • sqrt(50)

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