Cosine rule

Introduction

The law of cosines, often known as the cosine rule, is a formula that links the cosine to the three side lengths of a triangle. The rule of cosine aids in determining the link between the lengths of a triangle’s sides and the angles’ cosine. The Pythagoras theorem, which applies to a right triangle, is generalised by the cosine law in trigonometry.

Rule of cosine- statement

The square of any one of a triangle’s sides is equal to the difference between the sums of squares of the other two sides and double the product of the other sides and the cosine angle included between them, according to the rule of cosine.

The cosine rule has two applications:

• If we know the three side lengths of the given triangle, we can apply the cosine rule to get the three unknown angles.
• If we know two side lengths and the angle between them, we can apply the cosine rule to get the third side length of a triangle.

Cosine rule side formula

Consider the ABC oblique triangle below. A non-right triangle is known as an oblique triangle. Keep in mind that the side lengths are written in lowercase letters, while the angles are written in upper case letters.