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The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
The Official Table of Drops, formerly issued by the British Home Office, is a manual which is used to calculate the appropriate length of rope for long drop hangings. Following a series of failed hangings, including those of John Babbacombe Lee , a committee chaired by Henry Bruce, 1st Baron Aberdare was formed in 1886 to discover and report on ...
The angle θ is taken in the positive sense and must lie in the interval 0 < θ ≤ π (radian measure). The chord function can be related to the modern sine function, by taking one of the points to be (1,0), and the other point to be (cos θ, sin θ), and then using the Pythagorean theorem to calculate the chord length: [2]
For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio.
The arc length, from the familiar geometry of a circle, is = The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of ):
Angular diameter: the angle subtended by an object. The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of ...
(This is the angle α opposite the "rise" side of a triangle with a right angle between vertical rise and horizontal run.) as a percentage, the formula for which is which is equivalent to the tangent of the angle of inclination times 100. In Europe and the U.S. percentage "grade" is the most commonly used figure for describing slopes.
The angle bisector of the golden triangle subdivides the side that it meets in the golden ratio, and the areas of the two subdivided pieces are also in the golden ratio. [47] If the apex angle of the golden gnomon is trisected, the trisector again subdivides it into a smaller golden gnomon and a golden triangle. The trisector subdivides the ...