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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 ...
In geometry and geographical surveys, altitude helps create accurate topographic maps and understand the terrain's elevation. For high-altitude trekking and sports, knowing and adapting to altitude is vital for performance and safety.
For any interior point P, the sum of the lengths of the perpendiculars s + t + u equals the height of the equilateral triangle.. Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. [1]
An altitude of a triangle is a straight line through a vertex and perpendicular to the opposite side. This opposite side is called the base of the altitude, and the point where the altitude intersects the base (or its extension) is called the foot of the altitude. [23] The length of the altitude is the distance between the base and the vertex.
The precise standard meanings of latitude, longitude and altitude are currently defined by the World Geodetic System (WGS), and take into account the flattening of the Earth at the poles (about 21 km or 13 miles) and many other details. Planetary coordinate systems use formulations analogous to the geographic coordinate system.
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry . Analytic geometry is used in physics and engineering , and also in aviation , rocketry , space science , and spaceflight .
In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: The midpoint of each side of the triangle; The foot of each altitude
Lines A, B and C are concurrent in Y. In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.. The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil.