What is the pythagorean theorem? When does the Pythagorean theorem apply?

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

In other words, for the triangle shown below, a² + b² = c².

The legs, a and b, are the perpendicular sides of the right triangle and the hypotenuse, c, is the side opposite the right angle.

This application is frequently used in construction projects and basically anything that involves right triangles life roofs to a house and so on

For example, I have made a couple problems below that involves the pythagorean theorem and would be an example of a real world situation.