Displacement Question: Flat Earth vs. Spherical Earth

[Emethyst]

Homework Statement

Suppose a person has set up camp at the North Pole. If the person walks 8km south, then 3km east and finally 4km north, how far from the camp will the person be if a) it is assumed the Earth is flat? b) it is not assumed the Earth is flat.

Homework Equations

Pythagorean's theorem.

The Attempt at a Solution

I have solved for a) no problem (answer is 5km SE), the only part I'm having trouble with is b). Because no information is given concering a spherical Earth in the question, I'm guessing that it just might be a trick question, but I'm not sure. If someone can help me with part b) for this question it would be great, thanks in advance.

 

[Mentallic]

For a spherical Earth, if we go south 8km, go east 3km, then go north 8km then we end up back at the north pole. Can you see/understand why? So using the same idea, what if we only go north 4km?