I answered this one awhile back, but.....I'll go through it again
We need to use the Law of Cosines to first determine the distance from the pitcher to third base.....so we have
D = √ [ 47^2 + 63^2 - 2(47)(63) cos(45) ]
So......calling the angle "A" that the pitcher must turn, we have
sin A / 63 = sin (45) / D
sin A = 63 * sin (45) / √ [ 47^2 + 63^2 - 2(47)(63) cos(45) ]
arcsin ( 63 * sin (45) / √ [ 47^2 + 63^2 - 2(47)(63) cos(45) ] ) = A ≈ 86.8491°