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.

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

In a right triangle, the side opposite the right angle is the hypotenuse, and it is always the longest side.

To find the length of one side (a) when the hypotenuse (c) and the other side (b) are known, use the formula: a = √(c² - b²).

Using the formula: a = √(c² - b²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Using the formula: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.

The other two angles in a right triangle must add up to 90 degrees, making them complementary.

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and angles.

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.