General triangle. In general form of the triangle , the sides are denoted by , , and , and the angles are denoted by , , and .
Inscribed angle theorem. is called an inscribed angle, and is called a central angle. Then they have the following relationship:
Law of sines. Let is the radius of the circumscribed circle of , and let be the diameter of the circle.
Since by the inscribed angle theorem, we have ; thus, we obtain
Law of cosines. Let be perpendicular to . The square length can be expressed in terms of the sides and the angle via the two different right triangles and .
Comparing the rightmost expressions in (2-1)-(2-2),
In general we have
Heron's formula. Let be the area of , and let . By using via the law of cosines, we obtain