What is the cosine rule and when can it be used?

The cosine rule is used to find the length of a side or size of an angle. 

Take a look at the triangle below: 


For this triangle we have sides a, b and c and angles A,B and C. 


For this triangle the cosine rule can be written as: 


a2 = b2 + c2- 2bc Cos A


b2 = a2 + c2- 2ac Cos B


c2 = a2 + b2- 2ab Cos C


You use the above formula to work out a missing side of the triangle.


If you want to work out a missing angle, we rearrange the formula above to these:


cos A = b to the power 2 + c to the power 2 - a to the power 2 over 2 b c


cos B = a to the power 2 + c to the power 2 - b to the power 2 divided by 2 a c


cos C = a to the power 2 + b to the power 2 - c to the power 2


And we can use these formula to work out angles in the triangle. 


When to use the cosine rule:

Remember we can only use the cosine rule in 2 situations: 


1) If we already know 2 sides and 1 angle (shown below) 

image: triangle

2) If we already know 3 sides (shown below) 


Kulvinder  L. GCSE Maths tutor

2 years ago

Answered by Kulvinder , a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Katrina M. IB Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, A ...
£18 /hr

Katrina M.

Degree: Mathematics Bsc (Bachelors) - Exeter University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics
-Personal Statements-

“Hi, I am a patient, experienced and enthusiastic tutor ready to help each student reach their full potential.”

£20 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Extended Project Qualification

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

Arjun P. GCSE Economics tutor, A Level Economics tutor, 11 Plus Maths...
£18 /hr

Arjun P.

Degree: Politics, Philosophy and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Science+ 5 more

.TSA. Oxford.
-Personal Statements-

“I am a passionate and dedicated student, with over a year of tutoring experience. I am excited to help you improve!”

MyTutor guarantee

About the author

Kulvinder L.

Currently unavailable: for regular students

Degree: Medicine (Bachelors) - Kings, London University

Subjects offered:Maths, -Medical School Preparation-

-Medical School Preparation-

“Hi, I'm Kulvinder and I'm a 4th year Medical student at King's College London . I am currently completing my intercalated BSc in Imaging Sciences at King's.  I am extremley passionate and enthusiastic about Medicine, the Sciences and a ...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Solve the simultaneous equations x^2 + y^2 = 9 and x+ y = 2. Give your answer to 2.d.p

How do you differentiate x^x?

(2x + 3)/(x-4) - (2x - 8)/(2x + 1) = 1

Find the coordinates of the minimum point of the curve y=x^2+6x+5.

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss