Iwalk six miles in a straight line in a direction north of east, and i end up two miles east and several miles north. how many degrees north of east have i walked?

For this case we can model the problem as a rectangle triangle.
 We know:
 Length of the hypotenuse
 Length of one side of the triangle
 We want to know:
 Angle between the hypotenuse and the horizontal side of the triangle.
 For this, we use the following trigonometric relationship:
 
 
 You walked 70.5 degrees north of east