Law of Cosines Formula
Cosine Formula is the formula that gives the relation between the sides and the angles of the triangle. Suppose we are given a triangle in which the sides a, b, and c are given and A, B, and C are angles of the triangle respectively. Then the law of cosine formulas is,
- a2 = b2 + c2 – 2bc cos A
- b2 = a2 + c2 – 2ac cos B
- c2 = b2 + a2 – 2ba cos C
We can also find the angles of the triangle by the formulas,
- cos A = [b2 + c2 – a2]/2bc
- cos B = [a2 + c2 – b2]/2ac
- cos C = [b2 + a2 – c2]/2ab
Law of Cosines
Law of Cosines in Trigonometry is the fundamental law of mathematics used to find the angle of the triangle when all three sides of the triangle are given. This law is also called the Cosine Rule Or the Cosine Formula. If in a triangle the sides are a, b, and c, then law of cosine for angle A is given as:
a2 = b2 + c2 – 2bc cos A
Similarly, all other angles B and C are given. In this article, we will learn about, the Law of Cosines, the Law of Cosines formula, examples, and others in detail.
Table of Content
- What is Law of Cosines?
- Law of Cosines Formula
- Law of Cosines Proof
- How to Find Angle using Law of Cosines
- Sine Formula
- Examples Using Law of Cosines