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:

(3, 4, 5)

(5, 12, 13)

(6, 8, 10)

(7, 24, 25)

(8, 15, 17)

(9, 12, 15)

(9, 40, 41)

(10, 24, 26)

(12, 16, 20)

(12, 35, 37)

(14, 48, 50)

(15, 20, 25)

(15, 36, 39)

(16, 30, 34)

(18, 24, 30)

(20, 21, 29)

Right Triangle Formulas

Area

Area = (1/2) × base × height

Perimeter

Perimeter = a + b + c

Finding an Angle

θ = arctan(opposite/adjacent)

Frequently Asked Questions

Right Triangle Calculator