勾股定理计算器
以下详细说明暂以英文提供。
What the theorem says
In any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². Knowing any two sides is therefore enough to recover the third. To find the hypotenuse, add the squares of the legs and take the square root; to find a leg, subtract the known leg's square from the hypotenuse's square first. The subtraction only works when c is genuinely the longest side, which is why entries with c shorter than a leg are rejected.
Recognizing right triangles
The theorem runs both directions: if three lengths satisfy a² + b² = c², the triangle they form has a right angle between a and b. That is the principle behind the 3-4-5 rope trick used to square up corners on construction sites — any multiple such as 6-8-10 works too. Whole-number examples like these are rare enough that they have their own name, Pythagorean triples.
常见问题
Can I use this on a triangle without a right angle?
No. The plain theorem applies only when one angle is exactly 90°. For general triangles with three known sides, the triangle calculator uses the law of cosines instead.
Why was my leg rejected as "too long"?
A leg can never reach the hypotenuse, let alone exceed it — the hypotenuse faces the largest angle in the triangle. If your computed leg comes out longer than c, one of the entered values is probably mislabeled.