An example of modern architecture, designed with many right angles.

In geometry and trigonometry, a right angle is an angle of 90 degrees, corresponding to a quarter turn (that is, a quarter of a full circle). It can be defined as the angle such that twice that angle amounts to a half turn, or 180°.^[1]

Lines that are at a right angle to each other are perpendicular, an important geometrical property. The presence of a right angle in a triangle is the defining factor for right triangles.

A right angle may be expressed in different units:

• 90°
• ^π/₂ radians
• 100 grad (also called grade, gradian, or gon)
• 8 points (of a 32-point compass rose)
• 6 hours (astronomical hour angle)
• ∞% grade on the tangent scale
• 100% grade on the sine scale.

Symbolically a right angle is represented as two line segments joining in such a fashion, for example ∟ or ⦜.

In mathematics, right angle can be an additional unit of angle^[2]. 1r=90°=^π/₂ rad=100^g

The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line. Throughout history carpenters and masons have known a quick way to confirm if an angle is a true "right angle." It is based on the most widely known Pythagorean triple (3, 4, 5) and so called the "Rule of 3-4-5." From the angle in question, running a straight line along one side exactly three units in length, and along the second side exactly four units in length, will create a hypotenuse (the longer line opposite the right angle which connects the two measured endpoints) of exactly 5 units in length. This measurement can be made quickly and without technical instruments. The geometric law behind the measurement is the Pythagorean theorem ("The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides").

[edit] See also

• Cartesian coordinate system
• Orthogonality
• Perpendicular
• Rectangle
• Types of angles

[edit] References

1. ^ Lindahl, G. (1987). Euklides Geometri. Stockholm, Natur och kultur: ISBN 91-27-72185-X
2. ^ * convertworld.com angles