Pythagorean theorem and examples

**The Pythagorean theorem states that in a right 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.** It can be written as: c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

**Example 1:** In a right triangle with sides of length 3 units and 4 units, the length of the hypotenuse can be found using the Pythagorean theorem: **c^2 = 3^2 + 4^2 = 9 + 16 = 25, so c = sqrt(25) = 5.**

**Example 2:** In a right triangle with sides of length 5 units and 12 units, the length of the hypotenuse can be found using the Pythagorean theorem: **c^2 = 5^2 + 12^2 = 25 + 144 = 169, so c = sqrt(169) = 13.**

**Example 3:** In a right triangle with sides of length 8 units and 15 units, the length of the hypotenuse can be found using the Pythagorean theorem: **c^2 = 8^2 + 15^2 = 64 + 225 = 289, so c = sqrt(289) = 17.**