Right Triangle Calculator
Enter at least two sides to calculate all properties of the right triangle. Side C is the hypotenuse (longest side, opposite the 90° angle).
About Right Triangles
A right triangle is a triangle with one 90-degree angle. The side opposite the right angle is called the hypotenuse, and it's always the longest side. The other two sides are called legs.
Right triangles are fundamental in geometry and have many practical applications in construction, engineering, navigation, and physics.
The Pythagorean Theorem
a² + b² = c²
Where c is the hypotenuse, and a and b are the legs
This theorem, attributed to the ancient Greek mathematician Pythagoras, states that the square of the hypotenuse equals the sum of squares of the other two sides. It's one of the most famous theorems in mathematics.
Special Right Triangles
45-45-90 Triangle
An isosceles right triangle with two 45° angles.
Legs = a, Hypotenuse = a×√2
30-60-90 Triangle
A triangle with angles of 30°, 60°, and 90°.
Short : Long : Hypotenuse = 1 : √3 : 2
Common Pythagorean Triples
Pythagorean triples are sets of positive integers that satisfy a² + b² = c²:
Right Triangle Formulas
Area
Area = (1/2) × base × height
Perimeter
Perimeter = a + b + c
Finding an Angle
θ = arctan(opposite/adjacent)
Frequently Asked Questions
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