I think the requirement that direction only removed when found side by side should be stressed more in the kata description.
I took me a while to understand why ["NORTH", "WEST", "SOUTH", "EAST"] should not be reduced to [].

You maybe fogot to add a rule not to use built in function ? ))

There's smth wrong with the random test cases:
I do calculate all 3 angles and then do the 'switch case' like this
if (max(angles) <= 90): return 1 etc,

in some case I get error:
Acute triangles
[90.0, 90.0, 90.0]
2 should equal 1

or later I have same set of angles and different error:
Right triangles
[90.0, 90.0, 90.0]
1 should equal 2

it is assumed in test that the algorightm should search for the spaces in the string and first try to split it according to them if possible?
because 14,14,14,14,10 - fits spaces while 16,16,16,16,6 - does not