Answer:
A triangle does exist and is acute.
Explanation:
For three segments to work as the sides of a triangle, each length must be between the sum and difference of the other two lengths.
24 - 10 = 14
24 + 10 = 34
25 is between 14 and 34.
25 - 10 = 15
25 + 10 = 35
24 is between 15 and 35.
25 - 24 = 1
25 + 24 = 49
10 is between 1 and 49.
The three side lengths do form a triangle.
If the triangle is a right triangle, then the two shorter sides, 10 and 24 are the legs. The longest side is the hypotenuse. The Pythagorean must work.
10² + 24² = 676
25² = 525
Since 676 ≠ 525, the triangle is not a right triangle.
Since 525 < 676, the triangle is acute.
Answer: A triangle does exist and is acute.