Question 1033611
sin(x+y) = sin x cos y + sin y cos x
All we need are the cosines...
cos x = sqrt(1 - sin^2 x) = sqrt(1 - (3/5)^2) = 4/5
cos y = sqrt(1 - sin^2 y) = sqrt(1 - (12/37)^2) = 35/37
so that, when we plug in we get
sin(x+y) = 3/5 * 35/37 + 12/37 * 4/5 = 105/185 + 48/185 = 153/185