Pythagorean Theorem

The legs of a right triangle are the two sides that form the right angle, commonly referred to as sides 'a' and 'b'.

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

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). The formula is: $$c^2 = a^2 + b^2$$ .

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

The set 5, 12, 13 can form a right triangle because $$5^2 + 12^2 = 25 + 144 = 169 = 13^2$$ .

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

To find a missing side, use the Pythagorean Theorem: rearrange the formula to solve for the unknown side.

$$x = \text{sqrt}(21^2 - 15^2) = \text{sqrt}(441 - 225) = \text{sqrt}(216) = 14.7$$ .

A triangle is a right triangle if one of its angles measures 90 degrees.

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