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Pythagoras' theorem
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In any right-angled triangle, the three sides are linked by one famous rule. It lets you find a missing side.
The theorem
In a right-angled triangle with hypotenuse c (the longest side, opposite the right angle):
a2 + b2 = c2
3, 4, 5 works: 9 + 16 = 25.
a2 + b2 = c2
3, 4, 5 works: 9 + 16 = 25.
Finding the hypotenuse
Square the two shorter sides, add, then square root.
Sides 6 and 8: 36 + 64 = 100, √100 = 10.
Sides 6 and 8: 36 + 64 = 100, √100 = 10.
Finding a shorter side
Square the hypotenuse and the known side, subtract, then square root.
Hypotenuse 17, side 15: 289 − 225 = 64, √64 = 8.
Check: the hypotenuse must be the longest side.
Hypotenuse 17, side 15: 289 − 225 = 64, √64 = 8.
Check: the hypotenuse must be the longest side.
Find the distance between the points (1, 2) and (4, 6).
- Across: 4 − 1 = 3. Up: 6 − 2 = 4
- Distance2 = 32 + 42 = 25
- Distance = √25
Answer: 5 units
a2 + b2 = c2 where c is the hypotenuse. Add the squares to find the hypotenuse; subtract them to find a shorter side.
The interactive lesson includes the diagrams for this topic.
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