Finding the Hypotenuse

The hypotenuse is the side across from the right angle, and it is always the longest side of a right-angled triangle. In NSW Year 8 maths, Pythagoras' theorem \(c^2 = a^2 + b^2\) is used to find it from the two shorter sides (NESA outcome MA4‑PYT‑C‑01).

You will name the hypotenuse in a turned triangle, square and add the shorter sides, then take the square root, giving answers as whole numbers, surds such as \(\sqrt{149}\) or decimals rounded to one place. You will change units first and spot a common mistake. A gate brace, a bushwalk east then north and the sloping side of a trapezium are all found this way. It is part of Year 8 Pythagoras.