Calxsolver
Trigonometry

Pythagorean Theorem

The Pythagorean theorem relates the sides of a right triangle: a² + b² = c², where c is the hypotenuse. Enter any two sides and leave the third blank; the calculator solves for the missing one and shows the working.

Pythagorean Theorem

Find the missing side of a right triangle.

Try:
Answerc = 10
  1. Hypotenusec = √(a² + b²) = √(36 + 64) = 10
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Formula and method

a² + b² = c², c = √(a² + b²), a = √(c² − b²)

Enter any two sides and leave the unknown blank. If the hypotenuse c is unknown, compute c = √(a² + b²). If a leg is unknown, rearrange to get the missing leg = √(c² − known_leg²). The solver validates that the hypotenuse is strictly longer than either leg.

Worked examples

Find the hypotenuse with legs 6 and 8 Apply a² + b² = c² to find the missing hypotenuse. Find the missing leg when c = 13 and one leg is 5 Rearrange a² + b² = c² to solve for the unknown leg.

Key terms

Pythagorean theorem In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

Frequently asked questions

How do I use the calculator?

Enter the two sides you know and leave the unknown field blank. The solver fills in the missing side.

Can it find a leg, not just the hypotenuse?

Yes. If you know the hypotenuse and one leg, it computes the other leg as √(c² − leg²).

Why must the hypotenuse be the longest side?

In a right triangle the hypotenuse is always opposite the right angle and is longer than either leg.

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