① Finding the hypotenuseCalculator useful
The hypotenuse is the longest side and is opposite the right angle. Square the two shorter sides, add the squares, then take the square root.
② Finding a shorter sideCalculator useful
Square the hypotenuse and the known side, subtract the smaller square from the larger, then take the square root.
③ Is the triangle right-angled?Calculator useful
If the squares of the two shorter sides add up to the square of the longest side, the triangle has a right angle.
④ Using Pythagoras to solve problemsCalculator useful
The picture only sets the scene. Draw your own right-angled triangle from it, label the sides you know, then decide whether you need the hypotenuse or a shorter side.
⑤ Pythagoras in 3DCalculator usefulExtension
Look for right-angled triangles inside the solid. Drag a diagram to turn it round, or click it and use the arrow keys.
Key steps
Pythagoras' theorem: in a right-angled triangle, a² + b² = c², where c is the hypotenuse.
Finding the hypotenuse: add the squares of the two shorter sides, then square root.
Finding a shorter side: subtract the squares (hypotenuse − shorter side), then square root.
Rounding: when the answer is not exact, give lengths correct to 3 significant figures.
Checking: the hypotenuse must always be the longest side.