Final answer:
The Pythagorean Inequality Theorem for acute triangles asserts that for any acute triangle, the sum of the squares of the two shorter sides is greater than the square of the longest side.
Step-by-step explanation:
The Pythagorean Inequality Theorem for acute triangles is a principle related to the Pythagorean Theorem. While the Pythagorean Theorem itself states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b), the Pythagorean Inequality Theorem adapts this for acute triangles. It stipulates that for an acute triangle (a triangle where all angles are less than 90 degrees), the sum of the squares of the two shorter sides (a and b) is greater than the square of the longest side (c). In other words, a² + b² > c². This fact can be useful in a variety of applications, such as determining the shortest distance between two points, since forming a right triangle with the two legs representing the paths and the hypotenuse representing the shortest path applies the Pythagorean Theorem.