Law of cosines
![Figure 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.](/Images/godic/202501/06/Triangle_with_notations_2.svg3757.png")
![](/Images/godic/202501/06/Webysther_20160305_-_Ciclo_trigonométrico.svg3757.png")
![Fig. 2 – Obtuse triangle ABC with perpendicular BH](/Images/godic/202501/06/Obtuse_Triangle_With_Altitude_ZP2.svg3758.png")
![Fig. 3 – Applications of the law of cosines: unknown side and unknown angle.](/Images/godic/202501/06/Triangle-with-an-unknown-angle-or-side.svg3758.png")
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) 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.