What is the name for a triangle with one right angle?

A triangle with one right angle is called a right triangle. Its defining feature is a 90-degree angle, often marked with a small square in diagrams.

The side opposite the right angle is the hypotenuse, which is always the triangle’s longest side. The Pythagorean theorem connects the three sides: a² + b² = c², where c is the hypotenuse. A classic example is the 3-4-5 triangle, because 3² + 4² = 5².

Right triangles are central to geometry, surveying, architecture, navigation, and trigonometry. The sine, cosine, and tangent functions are commonly introduced by comparing the triangle’s side lengths with respect to one of its acute angles.

A common mix-up is thinking that “right” describes the triangle’s shape or size. It describes only its angle measurement. A right triangle can also be isosceles, such as a 45-45-90 triangle, or scalene, such as a 3-4-5 triangle. “Equilateral” is impossible because an equilateral triangle has three 60-degree angles.