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Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance (not the distance along the slope) and rise is the vertical distance.
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.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
is the angle between the slope line and the horizontal line, s is the slope distance measured between two points on the slope line, h is the height of the slope. = + Where L= Inclined length measured A= Inclined angle
Stream gradient (or stream slope) is the grade (or slope) of a stream. It is measured by the ratio of drop in elevation and horizontal distance. [ 1 ] It is a dimensionless quantity , usually expressed in units of meters per kilometer (m/km) or feet per mile (ft/mi); it may also be expressed in percent (%).
In these cases the distance to the base of the tree can be measured using the tape along the slope from eye level to the base of the tree and noting the slope angle Θ. In this case the height of the base of the tree above or below eye level is equal to the (sin Θ x slope distance) and the horizontal distance to the tree is (cos Θ x slope ...
It is an electronic transit theodolite integrated with electronic distance measurement (EDM) to measure both vertical and horizontal angles and the slope distance from the instrument to a particular point, and an on-board computer to collect data and perform triangulation calculations. [1]
The skier is then airborne until landing on the landing slope. The last part of the hill is the out-run, which may be either flat or even uphill, allowing the jumper to stop. The steepest point of the hill is the construction point , which is used to determine the score of a particular length.