Law of Sines
Author: Scott Farrar

Press Play at the bottom to see the Law of Sines constructed and proved for any triangle ABC.

a / 2r = sin(E)

E  =  A

sin(E) = sin(A)

a / 2r              = sin(A)

a / sin(A) = 2r

A similar argument holds for angles B and C.

2r = a / sin(A) = b / sin(B) = c / sin(C)

A = (0.3606519679596578, -2.6036488900061325)
B = (0.5383919872210869, -2.173330948636357)
C = (0.9159832243123526, -2.5097613391618188)
poly1, c, a, b = Polygon(A, B, C)
d = LineBisector(b)
δ = Angle(b, d)
e = LineBisector(c)
ε = Angle(c, e)
f = LineBisector(a)
ζ = Angle(a, f)
D = Intersect(d, f)
g = Circle(D, C)
h = Line(C, D)
E = Intersect(g, h, 2)
i = Segment(C, E)
j = Segment(E, B)
k = Line(B, E)
F = Point(k)
γ = Angle(E, B, C)
α = Angle(C, E, B)
η = Angle(C, E, F)
β = Angle(C, A, B)
poly2, c_1, b_1, e_1 = Polygon(B, E, C)