Math calculator

Pythagorean Theorem Calculator

Solve a right triangle for its hypotenuse or for one unknown leg. The calculation trail makes the reported missing side easier to reproduce.

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Working through Pythagorean Theorem with numbers

Tasks that depend on Pythagorean Theorem

The theorem checks squareness in construction, finds diagonals, converts coordinate changes to distance, and solves many navigation or layout problems on a flat plane.

What to notice in Pythagorean Theorem

Label the side opposite 90° as c. Square the known lengths, rearrange a² + b² = c² for the unknown, and take the positive square root because a physical length is positive. A hand-worked extension of Pythagorean Theorem is general triangle solving.

What belongs beside a Pythagorean Theorem answer

Link Unknown side to its Pythagorean Theorem role. Link Known leg to its Pythagorean Theorem role. The retained Pythagorean Theorem formula identifies the Pythagorean Theorem model.

Legs of 9 and 12 give c² = 81 + 144 = 225, so c = 15. Conversely, a known leg 9 and hypotenuse 15 give the other leg √(225 − 81) = 12. This Pythagorean Theorem example can be compared with coordinate distance.

In a right triangle, the squares of the two legs add to the square of the hypotenuse: a² + b² = c². The hypotenuse is opposite the right angle and is always the longest side.

Common interpretation traps for Pythagorean Theorem

This relationship only holds for right triangles. When finding a leg, subtract the known leg's square from the hypotenuse's square; reversing them creates an impossible negative radicand. If the Pythagorean Theorem assumptions do not fit, consider missing triangle angle.

Reviewing the Pythagorean Theorem case

Check Pythagorean Theorem from Unknown side, then verify Known leg. Estimate the Pythagorean Theorem Missing side before computing it again. If Other leg or hypotenuse changes during Pythagorean Theorem, keep Known leg fixed. That Pythagorean Theorem comparison shows whether Missing side moves as expected.

Before leaving the Pythagorean Theorem result

How do I identify the hypotenuse?

It is opposite the right angle and longer than either leg.

Can the theorem solve a non-right triangle?

No. Use trigonometric laws for general triangles.

Why take only the positive square root?

Side length represents a positive distance.

What is a Pythagorean triple?

A set of positive integers such as 3, 4, and 5 satisfying a² + b² = c².

Can decimals be entered?

Yes, as long as the known lengths are positive and geometrically possible.