Hypotenuse Calculator
Hypotenuse (c)
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Triangle Area
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Perimeter
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Angle A (degrees)
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Angle B (degrees)
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How to Calculate the Hypotenuse
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: c² = a² + b², so c = √(a² + b²). The hypotenuse is always the longest side, opposite the right angle.
This calculator also computes the triangle's area (A = ½ab for a right triangle), perimeter (a + b + c), and both acute angles using inverse tangent functions. All angles in a right triangle sum to 180°, with the right angle being 90°.
The Pythagorean theorem is one of the most important results in mathematics, with applications in navigation, construction, physics, and computer graphics. Common Pythagorean triples include (3,4,5), (5,12,13), and (8,15,17).
Frequently Asked Questions
What is the Pythagorean theorem?
c² = a² + b², where c is the hypotenuse and a, b are the other two sides of a right triangle. For sides 3 and 4, c = √(9+16) = √25 = 5.
What are Pythagorean triples?
Sets of three whole numbers that satisfy the Pythagorean theorem: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Any multiple of a triple is also a triple.
Can I find a missing leg instead of the hypotenuse?
Yes. If you know the hypotenuse c and one leg a, the other leg is b = √(c² - a²).
Does this work for non-right triangles?
The Pythagorean theorem only applies to right triangles. For other triangles, use the law of cosines: c² = a² + b² - 2ab·cos(C).