Calculate the length of any side of a right triangle using the Pythagorean theorem. Step-by-step solutions, triangle properties, and angle calculations.
Calculate the length of any side of a right triangle using the Pythagorean theorem:
Enter the lengths of two sides and leave the third as 0 to calculate it, or enter all three to verify it's a right triangle.
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The Pythagorean theorem is one of the most fundamental principles in geometry, named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
a² + b² = c²
Where c is the hypotenuse, and a and b are the legs
Our calculator can find any missing side of a right triangle when you know the other two sides. Simply enter the known side lengths and leave the unknown side as 0, or enter all three sides to verify if they form a right triangle.
Given: a = 3, b = 4
Find: c (hypotenuse)
Solution: c = √(3² + 4²) = √(9 + 16) = √25 = 5
Given: a = 5, c = 13
Find: b (other leg)
Solution: b = √(13² - 5²) = √(169 - 25) = √144 = 12
Some right triangles have special properties that make calculations easier and are commonly used in geometry and trigonometry.
Explore these related geometry calculators to solve more triangle and geometric problems:
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.
No, the Pythagorean theorem only applies to right triangles (triangles with one 90-degree angle). For other triangles, you would use the Law of Cosines or Law of Sines.
To find the hypotenuse, use the formula c = √(a² + b²) where a and b are the lengths of the other two sides.
To find a missing leg, rearrange the formula: a = √(c² - b²) or b = √(c² - a²) where c is the hypotenuse.
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, such as (3, 4, 5), (5, 12, 13), and (8, 15, 17).
The Pythagorean theorem is used in construction, navigation, computer graphics, engineering, and many other fields where distance calculations are needed.
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