To find the missing angles, we can use the properties of a triangle and the fact that the sum of angles in a triangle is always 180 degrees.

Given: AB = 5, angle B = 45 degrees, and angle C = 60 degrees

Find angle A:
Since A + B + C = 180 degrees (sum of angles in a triangle), we can substitute the given values:
A + 45 + 60 = 180
A + 105 = 180
A = 75 degrees

To find angle BS, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. Therefore:

sin(A)/BC = sin(B)/AC
sin(75)/BC = sin(45)/5
BC = 5sin(75)/sin(45)
BC ≈ 6.45

To find angle AS, we can use the Law of Sines again:
sin(A)/AC = sin(C)/BC
sin(75)/5 = sin(60)/6.45
AC = 5sin(60)/sin(75)
AC ≈ 4.28

Therefore, angle A is 75 degrees, angle BS is approximately 6.45, and angle AS is approximately 4.28 degrees.