What type of triangle has side lengths 12, 13, and 2√3

  obtuse

Step-by-step explanation:

The largest angle is about 99°, so the triangle is obtuse.

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If the side lengths given are a, b, and c, respectively, then angle B can be found from the Law of Cosines.

  b² = a² +c² -2ac·cos(B)

  cos(B) = (a² +c² -b²)/(2ac) = (12² +12 -13²)/(48√3) = -13/(48√3)

Note that this is negative, so we know the angle is more than 90° meaning the triangle is obtuse.

  B = arccos(-13/(48√3)) ≈ 98.996°

the answer is c. 23/3