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- Pythagoras' theorem
Pythagoras' theorem
Pythagoras' theorem links the three sides of any right-angled triangle. If you know two sides, you can always find the third.
Spot the hypotenuse
The hypotenuse is the longest side. It is always opposite the right angle.
The rule
a2 + b2 = c2
The two short sides squared add up to the hypotenuse squared.
The two short sides squared add up to the hypotenuse squared.
Long side or short side?
Finding the hypotenuse: square, add, square root.
Finding a shorter side: square, subtract, square root.
Sanity check: the hypotenuse must be the longest side.
Finding a shorter side: square, subtract, square root.
Sanity check: the hypotenuse must be the longest side.
A right-angled triangle has shorter sides 6 cm and 8 cm. Find the hypotenuse.
- Square: 62 = 36 and 82 = 64
- Add: 36 + 64 = 100
- Square root: √100 = 10
- 10 cm is longer than both other sides, so it makes sense.
Answer: 10 cm
a2 + b2 = c2, where c is the hypotenuse opposite the right angle. Long side: add. Short side: subtract. Then square root.
The interactive lesson includes the diagrams for this topic.
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