Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²).

The length of the hypotenuse is 5 cm, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

A right triangle is a triangle that has one angle measuring 90 degrees.

The legs of a right triangle are the two sides that form the right angle.

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem.

To find a missing leg (a or b), rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

A Pythagorean Triplet consists of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, such as (3, 4, 5) or (5, 12, 13).

The length of the other leg is 8 cm, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.