Answer:
obtuse
Explanation:
You want to know the type of triangle that has side lengths 12, 13, and √23.
Right triangle
Given leg lengths of √23 and 12, the Pythagorean theorem tells you the hypotenuse of a right triangle would be ...
(√23)² +12² = c²
23 + 144 = c² = 167
c = √167 ≈ 12.92
When the longest side (13) is longer than necessary for a right triangle (12.92), the largest angle is larger than 90°. The triangle is obtuse.
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Additional comment
The law of cosines can be used to find the largest angle. That relation is ...
C = arccos((a² +b² -c²)/(2ab))
C = arccos((23 +144 -169)/(2√23(12)) ≈ 91°
The largest angle is obtuse, so this is an obtuse triangle.
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