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In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of those two segments equals the altitude.
The process of drawing the altitude from a vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length (symbol b) equals the triangle's area: A = h b /2 ...
For example, the geometric mean of 2 and 3 is 2.45, while their arithmetic mean is 2.5. In particular, this means that when a set of non-identical numbers is subjected to a mean-preserving spread — that is, the elements of the set are "spread apart" more from each other while leaving the arithmetic mean unchanged — their geometric mean ...
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level (assumed zero geopotential) that represents the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. [1]
The exact definition and reference datum varies according to the context (e.g., aviation, geometry, geographical survey, sport, or atmospheric pressure). Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage.
altitude: "height where the chosen reference surface is mean sea level" [1] The International Civil Aviation Organization (ICAO) offers similar definitions: [2] altitude: "the vertical distance of a level, a point or an object considered as a point, measured from the mean sea level (MSL);" [2]
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