AQA GCSE Maths

Sine & cosine rule

AQA GCSE Maths revision on Sine & cosine rule. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.

Sample questions (3 of 16)

  1. Question 1

    In a non-right-angled triangle, you are given two sides and the included angle. Which method is most appropriate to find the length of the third side?

    • A) Sine rule
    • B) Cosine rule
    • C) Pythagoras' theorem
    • D) SOH CAH TOA
    Show answer

    Answer: Cosine rule

    Pythagoras' theorem and SOH CAH TOA only apply to right-angled triangles. When you have two sides and an angle trapped between them, the cosine rule acts as a generalisation of the Pythagoras' theorem for any triangle.

  2. Question 2

    A student attempts to solve for a missing side in a non-right-angled triangle using the sine rule but is given two sides and the included angle. Why is this method failing?

    • A) The sine rule requires at least one complete side-angle pair
    • B) The sine rule only works for obtuse triangles
    • C) The student forgot to square the sides
    • D) The sine rule is only for calculating angles
    Show answer

    Answer: The sine rule requires at least one complete side-angle pair

    The sine rule states that the ratio of a side to the sine of its opposite angle is constant across the triangle. If you have two sides and an included angle, you do not have a complete pair of an opposite side and angle, making the cosine rule the necessary choice.

  3. Question 3

    If you are given three sides of a triangle (SSS) and need to find an angle, what is the first step when using the cosine rule formula?

    • A) Square the sides
    • B) Rearrange the formula to make cos(A) the subject
    • C) Divide the sides by the sine of the angle
    • D) Use the sine rule instead
    Show answer

    Answer: Rearrange the formula to make cos(A) the subject

    The standard cosine rule formula is written to find a side length. To find an angle when all three sides are known, you must algebraically manipulate the formula to isolate the cosine of the angle before applying the inverse cosine function.

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13 more questions on Sine & cosine rule — plus mistakes tracking and spaced repetition across the whole Maths spec.

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