How do you use Pythagoras' Theorem to find a missing side?

To find a missing side using Pythagoras' Theorem, apply the formula \(a^2 + b^2 = c^2\) for right-angled triangles.

Pythagoras' Theorem is a fundamental principle in geometry that applies to right-angled triangles. It states that in such a 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. The formula is written as \(a^2 + b^2 = c^2\), where \(c\) represents the hypotenuse, and \(a\) and \(b\) are the other two sides.

To find a missing side, first identify which side you need to find: the hypotenuse or one of the other sides. If you need to find the hypotenuse, rearrange the formula to \(c = \sqrt{a^2 + b^2}\). For example, if one side is 3 units and the other is 4 units, calculate \(c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\) units.

If you need to find one of the other sides, rearrange the formula to solve for the missing side. For example, if the hypotenuse is 10 units and one side is 6 units, use \(a = \sqrt{c^2 - b^2}\). Calculate \(a = \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8\) units.

Remember to always check that the triangle is right-angled before using Pythagoras' Theorem, as it only applies in this case. Practising with different sets of numbers will help you become more comfortable with the process.