Pythagoras calculator
Hypotenuse from 5 and 7
8.60
Exactly √74, which is 8.60 to 2 decimal places.
Working
- The hypotenuse is the longest side, opposite the right angle: c² = a² + b².
- c² = 5² + 7² = 25 + 49 = 74.
- c = √74 = 8.60 (3 s.f.).
Your result
8.60. Exactly √74, which is 8.60 to 2 decimal places.
Pythagoras, step by step
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Your mock plan, in three taps
Pythagoras' theorem: hypotenuse² = a² + b². Sides of 5 cm and 7 cm give a hypotenuse of √74 = 8.60 cm (3 s.f.); for a shorter side, subtract the squares.
Questions people ask
How do you find the hypotenuse?
Square the two shorter sides, add them, and square root the total. 6 and 8: 36 + 64 = 100, √100 = 10.
How do you find a shorter side?
Square the hypotenuse, subtract the square of the other side, then square root. 13 and 5: 169 − 25 = 144, √144 = 12.
How do I know which side is the hypotenuse?
It is the longest side, opposite the right angle. It is always the one on its own in c² = a² + b².
What is a Pythagorean triple?
Three whole numbers that fit the theorem exactly, such as 3, 4, 5 and 5, 12, 13. Any multiple of one, like 6, 8, 10, is also a triple.
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How we work this out
What it does
Find the hypotenuse or a shorter side of a right-angled triangle, with the working and the exact answer.
Two side lengths of a right-angled triangle, above 0.
Method
- Hypotenuse: c² = a² + b², then square root.
- Shorter side: a² = c² − b², then square root.
- Answers to 3 significant figures, with the exact square root.