find the hypotenuse

Find the Hypotenuse

The hypotenuse is computed as c = √(a² + b²). It is the longest side, opposite the right angle (90°).

Leg a

Leg b

Hypotenuse c

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Why c = √(a²+b²)

The Pythagorean theorem states a²+b²=c². Isolating c: c = √(a²+b²). For a=3, b=4: c = √(9+16) = √25 = 5.

Examples

3-4-5 triple

Input: a=3, b=4
Expected output: c=5

Classic Pythagorean triple.

Isosceles triangle

Input: a=1, b=1
Expected output: c=√2 ≈ 1.4142

c = √2 (diagonal of unit square).

Full tool FAQ

What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: c² = a² + b². Attributed to Greek mathematician Pythagoras (~570–495 BC).

What is the hypotenuse?

What are the legs?

What is a Pythagorean triple?

How can I check whether a triangle is a right triangle?

Does the tool work with decimal values?

How precise is the result?

Does the theorem apply to non-right triangles?

Frequently asked questions

Can the hypotenuse be irrational?

Yes. For a=1, b=1, c=√2 is irrational. The tool displays the decimal approximation.

Does this page replace official or professional review?

No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.