Pythagoras review
Objective. Select and apply Pythagoras in two-dimensional problems.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Pythagoras' theorem relates the three sides of a right-angled triangle, stating that the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse. To find a missing hypotenuse, square both known shorter sides, add them together, then take the square root of the result. To find a missing shorter side instead, square the hypotenuse and the known shorter side, subtract the smaller from the larger, then take the square root. For example, with shorter sides 6 and 8, the hypotenuse is √(6² + 8²) = √(36+64) = √100 = 10.
Worked example
A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Use Pythagoras to find the other shorter side.
- 1Square both known sides: 13² = 169 and 5² = 25.
- 2Since this is a shorter side, subtract: 169 − 25.
- 3169 − 25 = 144.
- 4Take the square root: √144 = 12.
Answer: 12 cm
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes add the squares even when finding a shorter side, instead of subtracting, producing a hypotenuse-sized answer by mistake. Subtract when finding a shorter side; only add when finding the hypotenuse.
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