Properties of Cosine Rule

The properties of cosine rule are listed below

• To determine the side lengths of triangle ABC, we can express it as a² = b² + c² – 2bc cos α, b² = a² + c² – 2ac cos β and c² = b² + a² – 2ba cos γ.
• To calculate the angles of triangle ABC, the Cosine Rule is expressed in the following manner: cos α = [b² + c² – a²]/2bc, cos β = [a² + c² – b²]/2ac and cos γ = [b² + a² – c²]/2ab.
• Sine Rule is expressed as a/sin α = b/sin β = c/sin γ.
• Cosine Rule is also known as the Law of Cosines.
• Cosine Rule is a formula which helps to calculate the sides and angles of a triangle.
• Pythagoras Theorem is an application of the Cosine Rule which only holds true for right-angle triangles.
• The Cosine Rule can be applied or utilized in any triangle.

Where to use Cosine Rule?

The Cosine Rule is useful for finding:

• The third side of a triangle by using the lengths of two known sides and the angle formed between them.
• The angles of a triangle by using all three sides of the triangle.

Cosine Rule commonly referred to as the Law of Cosines in Trigonometry establishes a mathematical connection involving all three sides of a triangle and one of its angles. Cosine Rule is most useful for solving the unknown information of a triangle. For example, when all three sides of a triangle are known, the Cosine Rule allows the determining of any angle measurement. Similarly, if two sides and the included angle between them are known, this rule facilitates the calculation of the third side length.

The Cosine Rule is a relationship between the lengths of a triangle’s sides and the cosine of one of its angles, allowing us to calculate distances and angles. When computing the third side of a triangle if two sides and their included angle are given, and when computing the angles of a triangle if all three sides are known, in that case, the Cosine Rule plays a valuable role.

In this article, we will discuss the introduction, definition, properties, formula of the Cosine Rule, and its meaning. We will also understand the proof of the Cosine Rule. We will also solve various examples and provide practice questions based on Cosine Rule for a better understanding of the concept of this article.