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: $$a^2 + b^2 = c^2$$ .

To find the length of the hypotenuse (c) in a right triangle, use the formula: $$c = \text{sqrt}(a^2 + b^2)$$ .

The hypotenuse is the longest side of a right triangle, opposite the right angle.

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as side a and side b.

Using the Pythagorean Theorem: $$c = \text{sqrt}(3^2 + 4^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem: $$a^2 + b^2 = c^2$$ .

Using the Pythagorean Theorem: $$c = \text{sqrt}(6^2 + 8^2) = \text{sqrt}(36 + 64) = \text{sqrt}(100) = 10$$ .

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

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

Using the Pythagorean Theorem: $$b = \text{sqrt}(13^2 - 5^2) = \text{sqrt}(169 - 25) = \text{sqrt}(144) = 12$$ .