In trigonometry, the law of sines (or sine law) is a statement about arbitrary triangles in the plane. If the sides of the triangle are (lower-case) a, b and c and the angles opposite those sides are (capital) A, B and C, then the law of sines states
The reciprocal of the number described by the sine law (i.e. a/sin(A)) is equal to the diameter D of the triangle's circumcircle (the unique circle through the three points A, B and C). The law can therefore be written
Make a triangle with sides a, b, and c, and opposite angles A, B, and C. Make a line from the angle C to the opposite side c that cuts the original triangle into two right triangles, and call the length of this line h. Therefore: