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.