Basic relations between elements of triangle

Law of cosines. Law of sines. Law of tangents. 
Area formulas. Heron's  formula. 
Radii of circumscribed and inscribed circles.

Designations: a, b, c – sides;  A, B, C – angles of triangle;  p = ( a + b + c ) / 2  - a half-perimeter;  h – a height;  S – an area;  R, r  –  radii of circumscribed and inscribed circles correspondingly.

Law of cosines:

Law of sines:

Law of tangents:

 Area formulas:

Radii of circumscribed and inscribed circles: