Where can I download free the cosine rule PDF worksheets with answers?

On this MathsLinks page you can download free printable the cosine rule PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Maths4Everyone, Corbett Practice, Corbett Textbook, plus a printable one-page the cosine rule revision guide.

What GCSE grade is the cosine rule (7N)?

The cosine rule (topic code 7N) is a Grade 7 geometry topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free The cosine rule Worksheets (PDF) with Answers — GCSE Maths

Free The cosine rule PDF Worksheets & Answers

Grade 7 • Topic 7N

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Maths DIY Exam-style booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 7 topics
7A - Surds	7B - Bounds
7C - Proportion (harder)	7D - Algebraic fractions
7E - The quadratic formula	7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs	7H - Rearranging (harder)
7J - Functions (harder)	7K - Iteration
7L - Area of any triangle	7M - The sine rule
7N - The cosine rule	7P - Congruent triangles
7Q - 3D pythagoras / trig.	7R - Histograms
7S - Conditional probability	7T - Exact trig. values (harder)
7U - Area of a segment

Explanation:

Use the Cosine Rule when you do not have a complete opposite side-angle pair: either you know 2 sides and the included angle (SAS) and want the third side using a² = b² + c² − 2bc cos A, or you know all 3 sides (SSS) and want an angle using cos A = b² + c² − a²2bc.

Make sure the side labeled a is always the side directly opposite the angle A in the formula. Remember to take the square root at the end when finding a side length.

Example 1: Find side a when b = 7 cm, c = 10 cm, and included angle A = 58° (3 s.f.).

Solution:

a² = 7² + 10² − (2 × 7 × 10 × cos 58°)

a² = 149 − 140 cos 58° = 74.8112...

a = √74.8112... = 8.6493... cm

Answer: a = 8.65 cm (3 s.f.)

Example 2: A triangle has sides 6 cm, 8 cm, and 11 cm. Find the largest angle (1 d.p.).

Solution:

Largest angle A is opposite longest side (a = 11):

cos A = 6² + 8² − 11²2 × 6 × 8 = −2196

A = cos⁻¹(−0.21875) = 102.635...°

Answer: 102.6° (1 d.p.)

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper The cosine rule Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 AQA Jun 2025 2H Q18 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Lines AB, BC, CD and AD form two triangles.

Work out the length of AD.

Worked Solution & Mark Scheme (4 marks)

In bottom isosceles triangle: base angles are both 32°, so vertex angle = 180° – 2(32°) = 116° M1
Vertically opposite angle in top triangle = 116° M1
By Cosine Rule: AD² = 9.6² + 2.8² – 2(9.6)(2.8) cos(116°) = 100 + 23.567 = 123.567 M1
AD = √123.567 ≈ 11.1 cm. A1

Answer: Answer 11.1 cm

Past Paper Example 2 AQA Nov 2022 2H Q24 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

B is 60 miles from A on a bearing of 170°

A ship sails from A on a bearing of 247°
It travels at a constant speed of 23 mph for 112 hours.
Is the ship now closer to B than it was when it left A?
You **must** show your working.

Worked Solution & Mark Scheme (5 marks)

(Average speed = distance ÷ time)
Distance AC = 23 × 1.5 = 34.5 miles M2
Angle BAC = 247° – 170° = 77° M1
By Cosine Rule: BC² = 60² + 34.5² – 2 × 60 × 34.5 × cos 77° = 3600 + 1190.25 – 931.30 = 3858.95 M1
BC = √3858.95 = 62.1 miles > 60 miles, so No (it is further away). C1

Answer: Distance travelled = 23 × 1.5 = 34.5 miles. Angle at A = 247° – 170° = 77°.
Distance to B = √(60² + 34.5² – 2 × 60 × 34.5 × cos 77°) = 62.1 miles > 60 miles, so No.

Past Paper Example 3 GCSE Nov 2024 3H Q17 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is triangle ABC.

Work out the area of triangle ABC.
Give your answer correct to 3 significant figures.

Worked Solution & Mark Scheme (4 marks)

cos A = (14.6² + 7.9² – 18.2²) / (2 × 14.6 × 7.9) = –55.67 / 230.68 = –0.24133... ⇒ A = 103.965° M3
Area = 1/2 × 14.6 × 7.9 × sin(103.965°) = 55.967... = 56.0 cm² A1

Answer: 56.0 cm²

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The cosine rule

Free The cosine rule PDF Worksheets & Answers

Guide to The cosine rule: Explanation, Diagrams & Worked Examples

GCSE Past Paper The cosine rule Questions & Answers