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Let R be the radius of the arc which forms part of the perimeter of the segment, θ the central angle subtending the arc in radians, c the chord length, s the arc length, h the sagitta of the segment, d the apothem of the segment, and a the area of the segment. Usually, chord length and height are given or measured, and sometimes the arc length ...
Architects, engineers, and contractors use these equations to create "flattened" arcs that are used in curved walls, arched ceilings, bridges, and numerous other applications. The sagitta also has uses in physics where it is used, along with chord length, to calculate the radius of curvature of an accelerated particle.
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]
The radius of such a curve is 5729.57795. If the chord definition is used, each 100-unit chord length will sweep 1 degree with a radius of 5729.651 units, and the chord of the whole curve will be slightly shorter than 600 units.
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius , or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed ...
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
A standard chord length is used: in the UK this is conventionally 30 metres, or sometimes 20 metres. Half chords, i.e. 15 metre or 10 metre intervals, are marked on the datum rail using chalk. The string, which is one full chord long, is then held taut with one end on two marks at each end of a chord, and the offset at the half chord mark measured.