Law of cosines

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or Al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines statesProposition 12In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle. In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or Al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c. For the same figure, the other two relations are analogous: The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if the angle γ is a right angle (of measure 90 degrees, or π/2 radians), then cos γ = 0, and thus the law of cosines reduces to the Pythagorean theorem: