How it works

Pythagoras' theorem states that in a right-angled triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). To find the hypotenuse, add the squares of the other two sides and take the square root. To find a shorter side, subtract the square of the known short side from the square of the hypotenuse before square rooting.

The method

1. 1.Identify the hypotenuse (the side opposite the right angle)
2. 2.Decide whether you are finding the hypotenuse or a shorter side
3. 3.Use c² = a² + b² for the hypotenuse or a² = c² - b² for a shorter side
4. 4.Take the square root to find the final length

Worked example

Find the hypotenuse of a right triangle with shorter sides 6cm and 8cm.

1. c² = 6² + 8² = 36 + 64 = 100
2. c = √100 = 10cm

Worked example

A right triangle has hypotenuse 13cm and one side 5cm. Find the other side.

1. a² = 13² - 5² = 169 - 25 = 144
2. a = √144 = 12cm

Common mistakes

• Adding the squares when finding a shorter side instead of subtracting
• Misidentifying which side is the hypotenuse
• Forgetting to square root the final answer