Types of angles (age 13+)
Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
What a learner can do afterwards
- Calculate the hypotenuse of a right-angled triangle given the two shorter sides
- Find a shorter side given the hypotenuse and the other short side
- Use Pythagoras’ Theorem to find the distance between two points on a coordinate grid
The lesson
A right-angled triangle has one 90-degree angle. The longest side sits opposite that angle. This side is called the hypotenuse.
Pythagoras' Theorem links the three sides. If a and b are the two shorter sides and c is the hypotenuse, then a² + b² = c².
A ladder leans against a wall, meeting the ground at a right angle. The foot of the ladder is 6 m from the wall, and it reaches 8 m up. Add the squares of the two shorter sides: 6² + 8² = 36 + 64 = 100. Take the square root: c = 10. The ladder is 10 m long.
Only use a² + b² = c² on right-angled triangles. If you know the hypotenuse and want a shorter side, subtract instead: a² = c² - b².
In a right-angled triangle, a² + b² = c², where c is the hypotenuse: add the squares to find c, or subtract to find a shorter side.
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.