Aship is 45 miles east and 30 miles south of port. if the captain wants to sail directly to south port, what beating sold be taken

Probaly you meant  'what bearing should be taken'

so use pythagorean theorem
c=distance from position to south port
b=45
a=30

a^2=B^2=c^2
30^2+45^2=c^2
900+2025=c^2
2925=c^2
square root of both sides
15 times √13
aprox
54.08
54.1
opposite of east=west
opposite of south=north

bearing=
54.1 miles north-west