There are many uses for the Pythagorean Theorem, that is the main reason why it is important. You can use the Pythagorean Theorem to find out if a triangle is an acute triangle, obtuse triangle or a right triangle. If the Theorem works and the side lengths squared is equal to the hypotenuse squared, then it is a right triangle, if the hypotenuse squared is longer than the two side lengths squared and added together then the triangle is obtuse. If the hypotenuse squared is shorter than the two side lengths squared and added together then the triangle is acute.
Another reason the Pythagorean Theorem is imported is it can help you find missing side lengths. Not only can it help you find the third side length to a right triangle, but it can also help you find the missing side lengths to squares and rectangles when the triangles are pushed together. The pythagorean Theorem can help build rectangles and squares.
Builders use the Pythagorean Theorem to help keep right angles and build houses, decks, buildings, and to put windows, doors and floors in.