Year 10 Foundation · Pythagoras and trigonometry
Find the longest side of a right-angled triangle
Definition
In any right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c².
Why Do I Have to Learn This?
Pythagoras links the three sides of a right-angled triangle. Builders, sailors and game designers use it to find distances they cannot measure directly.
Key Rules:
- 1. It only works in right-angled triangles.
- 2. The hypotenuse, c, is always the side opposite the right angle and the longest.
- 3. To find a shorter side, rearrange: a² = c² − b².
Remember:
- •c is the hypotenuse, do not square the wrong side.
- •Remember to take the square root at the end to get the length itself.
- •Check it looks sensible: the hypotenuse must be the longest side.
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle. By Pythagoras' theorem, hypotenuse² = a² + b².
If the two shorter sides are 3 and 4, the hypotenuse is 5, because 3² + 4² = 5².
Animated Example:
Free Find the longest side of a right-angled triangle Worksheet
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Before this: Pythagoras’ theorem (Year 9) · Next: Angles, bearings and trigonometry (Year 11 Foundation)
Let’s Practise the Concept
Step 1 of 3
Sort by sides
Drag each shape into the right group.
4 sides
Not 4 sides