Law of Cosines

The law of cosines, also known as the cosine rule, is a mathematical relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles.  It is an extension of the Pythagorean theorem and can be used to solve triangles that are not right angled.  In simpler terms, the square of one side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of the two sides and the cosine of the included angle.

This law is useful when you know the lengths of two sides of a triangle and the measure of the angle between them and need to find the length of the third side.  It can also be used to find the measures of angles in a triangle when the lengths of all three sides are known.

The law has applications in various fields, including geometry, trigonometry, physics, and engineering, particularly in situations where angles and sides of non-right angled triangles need to be calculated or measured.

 

Law of Cosines Formulas

\( c^2= a^2+b^2-2ab\; cosC \) \( a^2= b^2+c^2-2ab\; cosA \) \( b^2= a^2+c^2-2ab\; cosB \)