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In China, Pei Xiu (224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances, [5] while Liu Hui (c. 263) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places.
The far-field range was the original antenna measurement technique, and the simplest; it consists of placing the antenna under test (AUT) a long distance away from the instrumentation antenna. Generally, the far-field distance or Fraunhofer distance , D F r n h , {\displaystyle \ D_{\mathsf {Frnh}}\ ,} is considered to be
Triangulation may be used to find the position of the ship when the positions of A and B are known. An observer at A measures the angle α, while the observer at B measures β. The position of any vertex of a triangle can be calculated if the position of one side, and two angles, are known.
Direction determination refers to the ways in which a cardinal direction or compass point can be determined in navigation and wayfinding. The most direct method is using a compass ( magnetic compass or gyrocompass ), but indirect methods exist, based on the Sun path (unaided or by using a watch or sundial ), the stars, and satellite navigation .
Tape measures are often used for measurement of smaller distances. 3D scanners and various forms of aerial imagery are also used. The theodolite is an instrument for the measurement of angles. It uses two separate circles, protractors or alidades to measure angles in the horizontal and the vertical plane. A telescope mounted on trunnions is ...
Many angle units are defined as a division of the turn. For example, the degree is defined such that one turn is 360 degrees. Using metric prefixes , the turn can be divided in 100 centiturns or 1000 milliturns, with each milliturn corresponding to an angle of 0.36°, which can also be written as 21′ 36″ .
An inclinometer or clinometer is an instrument used for measuring angles of slope, elevation, or depression of an object with respect to gravity's direction. It is also known as a tilt indicator , tilt sensor , tilt meter , slope alert , slope gauge , gradient meter , gradiometer , level gauge , level meter , declinometer , and pitch & roll ...
Measurement [ edit ] Since the angular distance (or separation) is conceptually identical to an angle, it is measured in the same units , such as degrees or radians , using instruments such as goniometers or optical instruments specially designed to point in well-defined directions and record the corresponding angles (such as telescopes ).