How to Find Angle using Law of Cosines
Law of Cosine is used to find the angles of the triangle when all three sides of the triangle are given. Suppose we are given a triangle with sides a, b, and c and angles of triangle are A, B, and C then angles of the triangle are calculated using the formula,
- cos A = [b2 + c2 – a2]/2bc
- cos B = [a2 + c2 – b2]/2ac
- cos C = [b2 + a2 – c2]/2ab
Example, Find ∠A of triangle ABC, where sides of triangles, a, b, and c, are 1 cm, 1 cm, and √2 cm.
Using cosine rule,
cos A = [b2 + c2 – a2]/2bc
⇒ cos A = {(1)2 + (√2)2 – (1)2}/2(1)(√2) = 2/2√(2)
⇒ cos A = 1/√(2)
⇒ A = cos-1(1/√(2)) = 45°
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
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