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Find a Side Using the Cosine Rule

In this worksheet, students will apply the cosine rule to find out lengths of missing sides of a non-right-angled triangle.

'Find a Side Using the Cosine Rule' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview

Ever wondered what these guys are going at the side of the road?

They are calculating distances  between one point and another using trigonometry.



Trigonometry is the study of angles and dimensions of triangles.

Unfortunately as schools tend not to have this specialist equipment, we are going to have to make do with the old fashioned method of pen and paper.

The cosine rule is used to calculate lengths in a non right angled triangle.  And here it is.

No... how on earth do you choose which one?

You may have been taught to label the triangle to find a, b or c and get really confused by it.

Try this, and you won't have to worry about labelling the triangle.


cosine rule simplified


You will need a scientific calculator in order to get the cos button. Make sure it is set to degrees.

Example 1


cosine rule example


We are given two side lengths and the trapped angle.


Square one side, and add the square of the other side.

Subtract 2 x side 1 x side 2 x Cos63(angle)

Square root your answer.



Example 2

cosine rule example

       Can you see that all you need are the two sides with the trapped angle? 

                                  When you use the angle, you will always use the COS button.

                                  As long as you remember the general formula you need not worry about a,b, or c                      


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