Law of Cosines

Generalizes the Pythagorean theorem to all triangles.

c^{2} = a^{2} + b^{2} - 2 ab cos C

Variables

When $C = 90°$ , $cos C = 0$ and it reduces to $a^{2} + b^{2} = c^{2}$ . Use it for SSS and SAS triangles.

$a = 5, b = 7, C = 60°$ : $c^{2} = 25 + 49 - 35 = 39$ , $c \approx 6.24$ .

Solve any triangle from SSS, SAS or ASA: all sides, angles, area, perimeter and type using the laws of sines and cosines.

Law of Sines

Relates sides to the sines of their opposite angles in any triangle.

Pythagorean Theorem

Relates the sides of a right triangle.