This archive report was first published on 13 June 2020.
What is the Law of Cosines? ¶
Published on June 13, 2020, the law of cosines is a theorem in trigonometry that describes the relationship between the lengths of the sides of a triangle and the cosine of one of its angles.
Also known as the formula with the cosine or cosine law, it states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the sides with the cosine of the angle between them.
For a triangle with sides a, b, and c, and an angle? between sides a and b, the law of cosines can be expressed as: c^2 = a^2 + b^2 - 2ab cos(?).
This theorem generalizes the Pythagorean theorem, which only applies to right triangles. The law of cosines is useful for calculating the third side of a triangle when the two sides and their closed angle are known, as well as for calculating the angles of a triangle when all three sides are known.
