Triangle Type

In this kata, you should calculate type of triangle with three given sides a, b and c (given in any order).

If all angles are less than 90°, this triangle is acute and function should return 1.

If one angle is strictly 90°, this triangle is right and function should return 2.

If one angle more than 90°, this triangle is obtuse and function should return 3.

If three sides cannot form triangle, or one angle is 180° (which turns triangle into segment) - function should return 0.

Input parameters are sides of given triangle. All input values are non-negative floating point or integer numbers (or both).

Acute

Right

Obtuse

Examples:

triangle_type(2, 4, 6) # return 0 (Not triangle)
triangle_type(8, 5, 7) # return 1 (Acute, angles are approx. 82°, 38° and 60°)
triangle_type(3, 4, 5) # return 2 (Right, angles are approx. 37°, 53° and exactly 90°)
triangle_type(7, 12, 8) # return 3 (Obtuse, angles are approx. 34°, 106° and 40°)

If you stuck, this can help you: http://en.wikipedia.org/wiki/Law_of_cosines. But you can solve this kata even without angle calculation.

There is very small chance of random test to fail due to round-off error, in such case resubmit your solution.

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# Should return triangle type:
#  0 : if triangle cannot be made with given sides
#  1 : acute triangle
#  2 : right triangle
#  3 : obtuse triangle

def triangle_type(a, b, c):
    alist=[a,b,c]
    alist=sorted(alist)
    print(alist)
    if alist[0]+alist[1]<=alist[2]:
        return 0
    if (alist[0]**2)+(alist[1]**2)==alist[2]**2:
        return 2
    elif (alist[0]**2)+(alist[1]**2)>alist[2]**2:
        return 1
    elif (alist[0]**2)+(alist[1]**2)<alist[2]**2:
        return 3