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°