Hypotenuse Calculator
Enter two legs to calculate the hypotenuse, angles, area, and perimeter.
Triangle Details
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This calculator finds the hypotenuse and other properties of a right triangle from two leg lengths.
- Enter leg a. Type the length of the first leg of the right triangle.
- Enter leg b. Type the length of the second leg.
- Read the results. The hypotenuse (c) is calculated using the Pythagorean theorem: c = sqrt(a^2 + b^2). The calculator also shows both acute angles, the area, and the perimeter.
Results update instantly as you type. Classic examples include the 3-4-5 and 5-12-13 right triangles.
About 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 two legs: a^2 + b^2 = c^2. This relationship was known to ancient civilizations and is one of the most fundamental results in geometry. The theorem only applies to right triangles (those with a 90-degree angle). The hypotenuse is always the longest side, opposite the right angle. This calculator also computes the acute angles using the arctangent function: angle A = arctan(a/b).
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse of a right triangle. To find the hypotenuse, take the square root of (a^2 + b^2). For example, with legs 3 and 4, c = sqrt(9 + 16) = sqrt(25) = 5.
What are Pythagorean triples?
Pythagorean triples are sets of three positive integers that satisfy a^2 + b^2 = c^2. Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Any multiple of a Pythagorean triple is also a valid triple, such as (6, 8, 10) from doubling (3, 4, 5).
Can I use this to find a missing leg?
This calculator is designed for finding the hypotenuse from two legs. To find a missing leg when you know the hypotenuse and one leg, use the Right Triangle Solver, which can solve for any missing values from any two known inputs.