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Identify the Triangle

Statement

 Goal

Given integer side lengths, determine if a triangle is acute, right, or obtuse provided it is not degenerate or impossible.
Input
Line 1: Three space separated integers a b and c for the lengths of each side, monotonically increasing.
Output
Line 1: A string indicating one of five distinct outcomes.

If the triangle has an area, classify it as:
acute if each angle is < 90°
right if one angle is 90°
obtuse if one angle is > 90°

Exceptional cases:
degenerate if the triangle is flat with no area
impossible if the triangle cannot be constructed
Constraints
0 < a <= b <= c < 100
Example
Input
3 4 5
Output
right

Game modes
Fastest, Shortest, Reverse

Test cases
Right Test
Input
3 4 5
Output
right

Validator 1 Validator
Input
12 35 37
Output
right

Obtuse Test
Input
5 12 15
Output
obtuse

Validator 2 Validator
Input
20 21 30
Output
obtuse

Acute Test
Input
6 8 9
Output
acute

Validator 3 Validator
Input
12 15 18
Output
acute

Degenerate Test
Input
1 2 3
Output
degenerate

Validator 4 Validator
Input
5 8 13
Output
degenerate

Impossible Test
Input
7 11 24
Output
impossible

Validator 5 Validator
Input
5 6 13
Output
impossible

Solution language

Solution

Stub generator input