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Pythagoras calculator: find the missing side.
Enter any two sides of a right-angled triangle and leave the third blank. You get the missing side, the area, the perimeter and both angles.
The theorem
In a right-angled triangle, the square of the longest side (the hypotenuse, c) equals the sum of the squares of the other two: a² + b² = c².
- Finding the hypotenuse: c = √(a² + b²). Sides 3 and 4 give c = √25 = 5.
- Finding a short side: a = √(c² − b²). With c = 13 and b = 5, a = √144 = 12.
Pythagorean triples to remember
Whole-number triples make quick checks: 3-4-5, 5-12-13, 8-15-17 and 7-24-25, and any multiple such as 6-8-10 or 9-12-15.
Real-life uses
Carpenters and builders use the 3-4-5 rule to check a corner is square: measure 3 units along one wall, 4 along the other, and the diagonal should be exactly 5. It also gives the length of a ladder needed to reach a height, or the true diagonal of a screen or a field.
FAQ
Common questions
Does Pythagoras' theorem work for every triangle?
Only for right-angled triangles. For other triangles you use the sine and cosine rules.
Which side is the hypotenuse?
The side opposite the right angle, which is always the longest side of the triangle.
What is a Pythagorean triple?
Three whole numbers that satisfy a² + b² = c², such as 3, 4, 5 or 5, 12, 13.
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Try it now: Pythagorean theorem
Eight quick questions with instant feedback. Your score is saved on this device and counts in the games and learning paths too.
Pythagorean theorem (Grade 8): Finding a side of a right-angled triangle using a² + b² = c². Open the practice page or print a worksheet.
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