The distance to the middle of the square from home plate = 63/√2 ≈ 44.55 ft
So.....we figure the angle thusly [ it will be < 90° ]
Distance picther is from 3rd [using Law of Cosines]
D^2 = 63^2 + [63/√2]^2 - 2(63)(63/√2)cos (45)
D = √[ 63^2 + [47]^2 - 2(63)(47)cos (45) ] ≈ 44.615 ft
So we can use the Law of Sines to find the angle, θ
sinθ/ 63 = sin45 / 44.615 → sinθ = 63 * sin45 / 44.615
arcsin [ 63 * sin45 / 44.615 ] = θ ≈ 86.85°
Here's a pic :

