Find the sides of the right triangle so that their sum is minimized

[MatinSAR]

What would be enough is assuming that North-South directions and East-West directions are mutually orthogonal everywhere in the area in question.

This is better.

If one starts at any point on that map and goes South, he follows a ray which goes from the North Pole and passes through the starting point.
If he goes East or West, he follows a circle which has its center at The North Pole and which passes through the starting point.

Thank you one more time for your help.

 

[SammyS]

It's not enough for the question you mentioned, But I guess it's enough to solve the main question which is related to high school. Do you agree? He doesn't walk that much(only 5 km) so the question doesn't want us to consider that he is walking on a sphere and ...

It does not really matter that @Hill disagrees.

The given problem, as you eventually stated in post #9, is quite clear. Your recent replies to @FactChecker reinforce that the given problem refers to 2D grid on a planar surface.

 

[MatinSAR]

It does not really matter that @Hill disagrees.

The given problem, as you eventually stated in post #9, is quite clear. Your recent replies to @FactChecker reinforce that the given problem refers to 2D grid on a planar surface.

Thank you @SammyS for your help.

Thank you to everyone who helped for his time.