Rightangle

Rightangle, more commonly written as right angle, denotes an angle of exactly 90 degrees. It is formed when two lines are perpendicular. In diagrams, a right angle is typically indicated by a small square at the vertex.

In Euclidean geometry, perpendicular lines determine four right angles around their intersection. An angle measuring 90 degrees is classified as a right angle. A right triangle is a triangle with one right angle; the side opposite the right angle is the hypotenuse, and Pythagoras’ theorem gives the relation a^2 + b^2 = c^2 between the lengths of the three sides.

Perpendicularity underpins many geometric constructions and coordinate systems. The x- and y-axes in a Cartesian plane are perpendicular, and many shapes, including rectangles, have interior right angles. In vector algebra, two vectors are perpendicular if their dot product is zero, a condition called orthogonality in a broader sense.

In trigonometry, the two non-right angles of a right-angled triangle are acute, and trigonometric ratios are defined with respect to these angles (for example, sine equals opposite over hypotenuse).

History and notation: the concept appears in ancient and classical geometry, with the conventional symbol for a right angle being a small square at the vertex in diagrams and texts.

See also: Perpendicular, Orthogonality, 90 degrees, Pythagorean theorem, Cartesian coordinate system, Right triangle.