The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In mathematical terms, a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This theorem has many applications in real life. For example, it is used in construction to ensure that structures are stable and secure. Engineers use the Pythagorean Theorem to calculate the lengths of beams and trusses in buildings and bridges. It is also used in navigation, with pilots and sailors using it to determine distances and angles between points. In addition, the Pythagorean Theorem is used in trigonometry to derive other important relationships, such as the sine, cosine, and tangent functions. These functions are essential in fields such as physics, engineering, and computer science. Overall, the Pythagorean Theorem is a fundamental concept in mathematics with wide-ranging applications in the real world. By understanding and applying this theorem, we can solve complex problems and make important calculations in various fields.