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Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of slopes of soil- and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. It is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit mining ...
It is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit mining, excavations, landfills etc.) and the equilibrium conditions. [ 1][ 2] Slope stability is the resistance of inclined surface to failure by sliding or collapsing. [ 3] The main objectives of slope stability analysis are ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) 'angle'), grad, or grade[ 1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees. [ 2][ 3][ 4] It is equivalent to 1 400 of a turn, [ 5] 9 10 of a ...
The Abney level is an easy to use, relatively inexpensive, and, when used correctly, an accurate surveying tool. Abney levels typically include scales graduated in measure degrees of arc, percent grade, and in topographic Abney levels, grade in feet per surveyor's chain, and chainage correction. The latter is the cosine of the angle, used to ...
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.
Triangulation. Estimating the height of a mountain using triangulation. A triangulation station signed by iron rod [ 1] In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.
Trigonometry. In trigonometry, the law of tangents or tangent rule[ 1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective sides.