What is the formula for Pythagoras' Theorem?

The formula for Pythagoras' Theorem is \(a^2 + b^2 = c^2\).

Pythagoras' Theorem is a fundamental principle in geometry, particularly in the study of right-angled triangles. According to the theorem, in any right-angled 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 lengths of the other two sides. Here, \(a\) and \(b\) represent the lengths of the two shorter sides, and \(c\) represents the length of the hypotenuse.

To use Pythagoras' Theorem, you first need to identify the right-angled triangle and label the sides appropriately. For example, if you have a triangle with sides of lengths 3 cm, 4 cm, and 5 cm, and you know it is a right-angled triangle, you can check if these lengths satisfy the theorem. According to the formula, you would calculate \(3^2 + 4^2\) and see if it equals \(5^2\). Indeed, \(9 + 16 = 25\), which confirms that the triangle is right-angled.

This theorem is incredibly useful for solving problems where you need to find the length of one side of a right-angled triangle when the lengths of the other two sides are known. It also helps in various applications such as construction, navigation, and even in computer graphics. Remember, Pythagoras' Theorem only applies to right-angled triangles, so always ensure you are working with one before using the formula.