The given triangle has side lengths of 8, 11, and 12 which are not equal. Therefore, the triangle is scalene.
To determine the classification by angles, we need to compare the measures of the angles with the thresholds for acute, right, or obtuse.
- If all angles are less than 90 degrees, the triangle is acute.
- If one angle is exactly 90 degrees, the triangle is right.
- If one angle is greater than 90 degrees, the triangle is obtuse.
The angle measurements in the given triangle are not enough to determine if it is acute, right or obtuse, but they can be used to narrow down the possibilities.
We know that the sum of angles in any triangle is 180 degrees. Therefore, we can use the given angle measures to determine if the triangle is acute or obtuse.
If the sum of the two smaller angles is greater than 90 degrees, then the third angle must be less than 90 degrees, and the triangle is acute. If the sum of the two smaller angles is less than 90 degrees, then the third angle must be greater than 90 degrees, and the triangle is obtuse.
Let's add up the two smaller angles in this triangle:
8 and 11 are the two smaller sides. If we compare them to the largest side (12), 8 and 11 are the smaller sides.
So the two smaller angles are 75 and 40 degrees.
75 + 40 = 115
Since 115 < 90 × 2, we know that the third angle must be greater than 90 degrees. Therefore, the triangle is an obtuse scalene triangle.