Henri Gautier, a French Royal Engineer, recognized the " natural slope " of different soils in 1717, an idea later known as the soil's angle of repose.

Reflection derivation, together with trigonometric angle addition rules, leads to the result that the reflected ray has a slope of

The angle θ a line makes with the positive x axis is closely related to the slope m via the tangent function:

One is by the angle in degrees, and the other is by the slope in a percentage.

The formulae for converting a slope as a percentage into an angle in degrees and vice versa are:

In the context of the standard unit circle with radius 1, where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component ( rise ) of the triangle, the cosine gives the length of the x-component ( run ), and the tangent function gives the slope ( y-component divided by the x-component ).

* Roof pitch relates to the slope and inclination angle

* Critical angle of repose, in engineering ; the steepest angle of descent of a slope when the material is on the verge of sliding

Chalk hills, known as chalk downland, usually form where bands of chalk reach the surface at an angle, so forming a scarp slope.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

However, in plane mapping there are two other angles to consider: the hyperbolic angle and the slope, which is the analogue of angle for dual numbers.

The average angle of slope on which it grows is 35 degrees, ranging from level to 90 degrees, although these extremes are uncommon.

As " percent " it is used to describe the steepness of the slope of a road or railway, formula for which is which could also be expressed as the tangent of the angle of inclination times 100.

Skylights admit harsh direct overhead sunlight and glare either horizontally ( a flat roof ) or pitched at the same angle as the roof slope.

Some of the morphological characteristics used to classify avalanches include the type of snow involved, the nature of the failure, the sliding surface, the propagation mechanism of the failure, the trigger of the avalanche, the slope angle, slope aspect, and elevation.

A powder snow avalanche is a turbulent cloud of snow and air that forms when an avalanche travels over an abrupt change in slope angle, such as a cliff band.

The angle of the slope that can hold snow, called the angle of repose, depends on a variety of factors such as crystal form and moisture content.

But when the incidence of human triggered avalanches are normalized by the rates of recreational use hazard increases uniformly with slope angle, and no significant difference in hazard for a given exposure direction can be found.

The rule of thumb is: A slope that is flat enough to hold snow but steep enough to ski has the potential to generate an avalanche, regardless of the angle.

This angle of just where the Orioles can look for improvement this year is an interesting one.

If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.

Merchant has found that the same basic relationships which describe the geometry and force systems in the case of the cutting mechanism can also be applied to the discontinuous chip formation provided the proper values of instantaneous shear angle and instantaneous chip thickness or cross-sectional area are used.

A sufficiently good approximation for determining the end reflection losses R can be obtained from the angle independent Fresnel formula: Af.

With integration, the effect of a small acceleration ( or small platform tilt angle ) can be seen after a time.

The angle between those lines can be measured, and is the angular separation between the two stars.

Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures.

The stock is hinged so the flukes can orient toward the bottom ( and on some designs may be adjusted for an optimal angle depending on the bottom type ).

Similarly, the angle that a line makes with the horizontal can be defined by the formula

6 ) at a finite distance from the axis ( or with an infinitely distant object, a point which subtends a finite angle at the system ) is, in general, even then not sharply reproduced, if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop ; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil.

3D beading generally uses the techniques of bead weaving, which can be further divided into right angle weave and peyote stitch.

* Lenses for the Canon EF mount, introduced with the company's EOS family of film SLRs in 1987 and used to this day on Canon full-frame and APS-H EOS DSLRs, can function fully on the company's APS-C DSLRs that use the EF-S mount ( although their angle of view will be different on the smaller APS-C sensor ).

Asymmetry can be manifested in the size of the breast, the position of the nipple-areola complex ( NAC ), the angle of the breast, and the position of the inframammary fold, where the breast meets the chest.

The apex of the breast, which includes the nipple, can have a flat angle of projection ( 180 degrees ) or acute angle of projection ( greater than 180 degrees ).

To insure that this resultant is normal to the surface of the water, and therefore can be effectively nulled by the force of the water beneath, the normal to the surface must have the same angle, that is,

The quantum hall effect is another example of measurements with high magnetic fields where topological properties such as Chern-Simons angle can be measured experimentally.

Most LCDs also have poorer color rendition and can change color with viewing angle, though modern PVA and IPS LCDs have greatly attenuated these problems.

In two dimensions the position vector which has magnitude ( length ) and directed at an angle above the x-axis can be expressed in Cartesian coordinates using the unit vectors and:

* Viewing angle is the maximum angle at which images on the monitor can be viewed, without excessive degradation to the image.

The disc remains in motion while travelling on its edge at a slight angle, and can travel exceedingly far in ideal situations.

For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.

Farkas speculated that the horn should be held in a downward angle to allow the air stream to go straight into the mouthpiece, although his later text shows that air stream direction actually is either upstream or downstream and is dependent upon the ratio of upper or lower lip inside the mouthpiece, not the horn angle.

Modern acrobatic kites use two or four lines to allow fine control of the kite's angle to the wind.

Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the angle between two vectors.

With the viewing angle and rotation rate of Vega now better known, this will allow for improved instrument calibrations.

Modern CAD packages can also frequently allow rotations in three dimensions, allowing viewing of a designed object from any desired angle, even from the inside looking out.

The power transmitted by an AC line increases as the phase angle between source end voltage and destination ends increases, but too great a phase angle will allow the generators at either end of the line to fall out of step.

Gas lasers typically use a window tilted at Brewster's angle to allow the beam to leave the laser tube.

The observations allow the determination of a measure of the Earth's angle with respect to the ICRF, called the Earth Rotation Angle ( ERA, which serves as a modern replacement for Greenwich Mean Sidereal Time ).

The law is also satisfied in metamaterials, which allow light to be bent " backward " at a negative angle of refraction ( negative refractive index ).

Multiturn potentiometers, both user-accessible and preset, allow finer adjustments ; rotation through the same angle changes the setting by typically a tenth as much as for a simple rotary potentiometer.

Firing at a moving target requires aiming ahead of the target ( which involves the so-called lead angle ) to allow for the time the bullets require to reach the vicinity of the target.

For example, cars often allow toe-in, camber and caster angle adjustments, just like their real-life counterparts.

The arm angle may be adjustable to allow the viewing angle to be adjusted.

Paul instructed surgeons, brought in from Los Angeles, to set his arm at an angle — just under 90 degrees — that would allow him to cradle and pick the guitar.

It would also allow them to approach record companies again from a different angle.

Professional video cameras often allow selecting shutter speed in terms of shutter angle instead of time units, especially those that are capable of overcranking or undercranking.

Using a five-throw crankshaft and 72 ° bank angle the firing order can be made even, and the two balanced shafts do not balance each other completely, but are combined into a single A 36 ° degree bank angle and a 108 ° flying arm crankshaft would allow even firing without a balance shaft and smaller counterweights, but would be impractical.

Wings are typically mounted at a small positive angle of incidence, to allow the fuselage to be have a low angle with the airflow in cruising flight.

However, today's modern reactive resin bowling balls now allow strokers to hit the " pocket " at a relatively high angle.