Jill rides her horse 5 miles due north and 3 miles due east. What is magnitude and direction of her ride

First magnitude ...

d^2=5^2+3^2

d^2=25+9

d^2=34

d=√34

now for direction ...

tanα=y/x

α=arctan (y/x) and we know y=5 and x=3 so

α=arctan (5/3)

α≈59.03624

So the vector of her ride is:

√34, 59.03624° or if you prefer ...

√34, 59°2'10" (in standard angle position)