In triangle ABC, sin A = 4/5. Find cos B.

Using the Law of Sines

sin A / 19  =sin B  / 9

(4/5) / 19  = sin B  / 9

sin B =  9(4/5) / 19

sin B =  36 / 95

cos B    = sqrt [   1 - sin^2 B ] 

cos  B = sqrt [  1 - (36/95)^2 ]  =  sqrt [ 95^2 - 36^2 ] / 95  = sqrt [ 7729 ] / 95