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where angle is in degrees and the trigonometric functions operate in degrees. For example, a slope of 100% or 1000‰ is an angle of 45°. A third way is to give one unit of rise in say 10, 20, 50 or 100 horizontal units, e.g. 1:10. 1:20, 1:50 or 1:100 (or "1 in 10", "1 in 20", etc.) 1:10 is steeper than 1:20. For example, steepness of 20% ...
Grade (slope) The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper ...
Small-angle approximation. Approximately equal behavior of some (trigonometric) functions for x → 0. The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: These approximations have a wide range of uses in branches of ...
Tobler's hiking function – walking speed vs. slope angle chart. Tobler's hiking function is an exponential function determining the hiking speed, taking into account the slope angle. [1][2][3] It was formulated by Waldo Tobler. This function was estimated from empirical data of Eduard Imhof.
Inscribed angle theorem for an ellipse Like a circle, such an ellipse is determined by three points not on a line. For this family of ellipses, one introduces the following q-analog angle measure, which is not a function of the usual angle measure θ : [ 16 ] [ 17 ]
Snell's law. Refraction of light at the interface between two media of different refractive indices, with n 2 > n 1. Since the velocity is lower in the second medium (v 2 < v 1), the angle of refraction θ 2 is less than the angle of incidence θ 1; that is, the ray in the higher-index medium is closer to the normal.
The angle of internal friction is thus closely related to the maximum stable slope angle, often called the angle of repose. But in addition to friction, soil derives significant shear resistance from interlocking of grains. If the grains are densely packed, the grains tend to spread apart from each other as they are subject to shear strain.
Hypotenuse. A right-angled triangle and its hypotenuse. In geometry, a hypotenuse is the side of a right triangle opposite the right angle. [1] It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. The length of the hypotenuse can be found using the Pythagorean theorem, which ...