Geometry

Law of Cosines

5^2 = 4^2 + 7^2 - 2(4 * 7) cos (ABC)

[5^2 - 4^2 - 7^2 ] / [-2 (4 * 7]  = cos ABC

-40 / -56 = cos ABC  =  5 / 8

sin ABC =   sqrt [ 8^2 - 5^2 ] / 8  =   sqrt [39 ] / 8