Side-Angle Formulas

Formulas expressing side lengths a, b, c of a triangle through trigonometric functions of the opposite angles  < A, < B and < C.

 
Law of sinus

 

 

Law of cosinus

(a / sin A) = (b / sin B) = (c / sinC)
a2 =  b2 + c2 - 2 b c cos A
b2 =  a2 + c2 - 2 a c cos B
c2 =  a2 + b2 - 2 a b cos C
Newton's Formulas Mollweide's Formulas
(b + c) / a = {cos [ (B - C) / 2]} / {sin ( A / 2 )}
(c + a) / b = { cos [ (C - A) / 2]} / {sin ( B / 2 )}
(a + b) / c = { cos [ (A - B) / 2]} / {sin ( C / 2 )}
(b - c) / a = {sin [ (B - C) / 2]} / {cos ( A / 2 )}
(c - a) / b = { sin [ (C - A) / 2]} / {cos ( B / 2 )}
(a - b) / c = { sin [ (A - B) / 2]} / {cos ( C / 2 )}
(b + c) / a = {cos [ (B - C) / 2]} / {sin ( A / 2 )}
(c + a) / b = { cos [ (C - A) / 2]} / {sin ( B / 2 )}
(a + b) / c = { cos [ (A - B) / 2]} / {sin ( C / 2 )}
(b - c) / a = {sin [ (B - C) / 2]} / {cos ( A / 2 )}
(c - a) / b = { sin [ (C - A) / 2]} / {cos ( B / 2 )}
(a - b) / c = { sin [ (A - B) / 2]} / {cos ( C / 2 )}