north = pt barrow, alaska
west = nihau is , hawaii
east = calais , maine
south = ka lae pt, hawaii

at least thats the best i can do with the map i have

Wrong. z-axis = constant. We have a 3-d world to work with.

teener pay attention to the international date line...

edit;
better map at home
west = near islands , alaska
east = some point east of Eastport , maine

Wrong?
An arc is 3d.

A line is the shortest distance between two points in space with infinite points along it but has no real dimension. it does not curve, it is not a plane, it is a line. It is two dimensional.

If you started at the north pole and went straight out, you would be in space. Make a right turn and then another, you would still be in space.
Following the curvature of the earth is an arc and not a line.

I thought the eastern most point was West Quoddy, in Maine

Yes, yes, yes, they aren't straight lines, and it isn't really a triangle, but to the person that did the travelling that was the perception, 3 straight lines, 3 90* angles and a triangle. It's all about perception. It's not a straight answer, it's a riddle. Trying to imagine worlds of 2D or >3D is interesting and difficult. I'm reading Flatland, by Edwin A. Abbott right now. Interesting book.

What kind of cookies were you eating?