피타고라스 정리 계산기

Q: What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It lets you find any missing side when you know the other two.

Q: How do I find the hypotenuse?

Use c = √(a² + b²). Square both legs, add the results, then take the square root. For example, if a = 6 and b = 8: c = √(36 + 64) = √100 = 10.

Q: Can I use this for non-right triangles?

No, the Pythagorean theorem only applies to right triangles (triangles with a 90° angle). For non-right triangles, use the Law of Cosines: c² = a² + b² − 2ab·cos(C).

Q: What are Pythagorean triples?

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Q: How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and is always opposite the right angle (90°). In the formula a² + b² = c², c is always the hypotenuse.

직각삼각형을 풉니다. 두 변을 입력하면 나머지 변을 계산합니다.

피타고라스 정리 계산기이란?

The Pythagorean theorem is one of the most fundamental and widely used results in all of mathematics. It states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².

This calculator lets you solve a right triangle in three ways: find the hypotenuse when you know both legs, find one leg when you know the other leg and the hypotenuse, or verify whether three given sides form a valid right triangle. Every result includes the area, perimeter, and a complete step-by-step derivation so you can follow the algebra.

공식

Pythagorean Theorem: a² + b² = c²

Finding the hypotenuse: c = √(a² + b²)

Finding leg a: a = √(c² - b²)

Finding leg b: b = √(c² - a²)

Area: A = ½ab

Perimeter: P = a + b + c

계산 방법

Choose what you want to find: the hypotenuse or one of the legs.
Enter the two known side lengths.
The calculator applies the Pythagorean theorem and shows the full algebraic derivation.
Review the area and perimeter of the right triangle.

예시

For a right triangle with legs a = 3 and b = 4: c = √(3² + 4²) = √(9 + 16) = √25 = 5. Area = ½ × 3 × 4 = 6 square units. Perimeter = 3 + 4 + 5 = 12 units.

주요 이점

Three solving modes: find hypotenuse, find leg a, or find leg b
Animated SVG right triangle visualization with labeled sides
Full step-by-step algebraic derivation using KaTeX-rendered formulas
Instant area and perimeter calculation
Copy, share, and export results with one click

피해야 할 일반적인 실수

Applying the theorem to non-right triangles — it only works for 90° angles
Confusing which side is the hypotenuse — it is always the longest side, opposite the right angle
Subtracting when you should add (or vice versa) — remember: c² = a² + b² to find c, but a² = c² − b² to find a leg
Forgetting to take the square root after adding or subtracting the squares

전문가 팁

Use Pythagorean triples (3-4-5, 5-12-13, 8-15-17) to quickly check your work
The hypotenuse is always the longest side of a right triangle
If a² + b² > c², the triangle is acute; if a² + b² < c², it is obtuse
For coordinate geometry, the distance between two points is just the hypotenuse of a right triangle formed by the horizontal and vertical differences

주요 용어 설명

빗변: The longest side of a right triangle, opposite the right angle
변: Either of the two shorter sides of a right triangle that form the right angle
피타고라스 수: Three positive integers a, b, c that satisfy a² + b² = c²
직각삼각형: A triangle with exactly one 90° angle
제곱근: The inverse operation of squaring a number

일반적인 사용 사례

Solving geometry homework and exam problems
Construction — calculating diagonal distances
Navigation — finding straight-line distances between two points
Architecture — verifying right angles in building layouts
Physics — resolving vector components

자주 묻는 질문

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It lets you find any missing side when you know the other two.

How do I find the hypotenuse?

Use c = √(a² + b²). Square both legs, add the results, then take the square root. For example, if a = 6 and b = 8: c = √(36 + 64) = √100 = 10.

Can I use this for non-right triangles?

No, the Pythagorean theorem only applies to right triangles (triangles with a 90° angle). For non-right triangles, use the Law of Cosines: c² = a² + b² − 2ab·cos(C).

What are Pythagorean triples?

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and is always opposite the right angle (90°). In the formula a² + b² = c², c is always the hypotenuse.

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주요 용어 설명

일반적인 사용 사례

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피타고라스 정리 계산기

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공식

계산 방법

예시

주요 이점

피해야 할 일반적인 실수

전문가 팁

주요 용어 설명

일반적인 사용 사례

자주 묻는 질문

관련 도구