Finding a Shorter Side

When the missing side is not the hypotenuse, Pythagoras' theorem is rearranged to \(b^2 = c^2 - a^2\). In NSW Year 8 maths you take the square of the known shorter side away from the square of the hypotenuse, then find the square root (NESA outcome MA4‑PYT‑C‑01).

You will pick out the hypotenuse first, find shorter sides with whole-number, decimal and surd answers, and round to one decimal place. You will check that each answer is shorter than the hypotenuse and fix a student's working that added instead of subtracting. The height of a playground slide, the width of a pool and the wires holding up a mast are all shorter sides. It is part of Year 8 Pythagoras.