The Cosine Rule

For the following triangle:

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The cosine rule says that:


In words, this means that, “a squared is equal to the sum of the squares of the other two sides in the triangle, minus two times the product of the other two sides times cos of the angle opposite a.

The cosine rule does not need a right angle in the triangle to work.

Cosine rule question

Find length a:



Don’t forget to take the square root! Note that I have only taken the positive answer, as a negative side length does not make sense in this situation.

In general the cos rule is used to find the length of one side, when you know:

·         The length of the two other sides in the triangle

·         The angle between these two other sides.