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Roof pitch is the steepness of a roof expressed as a ratio of inch(es) rise per horizontal foot (or their metric equivalent), or as the angle in degrees its surface deviates from the horizontal. A flat roof has a pitch of zero in either instance; all other roofs are pitched .
But in practice the usual way to calculate slope is to measure the distance along the slope and the vertical rise, and calculate the horizontal run from that, in order to calculate the grade (100% × rise/run) or standard slope (rise/run). When the angle of inclination is small, using the slope length rather than the horizontal displacement (i ...
Bonnet roof: A reversed gambrel or Mansard roof with the lower portion at a lower pitch than the upper portion. Monitor roof: A roof with a monitor; 'a raised structure running part or all of the way along the ridge of a double-pitched roof, with its own roof running parallel with the main roof.'
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.
To calculate the azimuth of the Sun or a star given its declination and hour angle at a specific location, modify the formula for a spherical Earth. Replace φ 2 with declination and longitude difference with hour angle, and change the sign (since the hour angle is positive westward instead of east).
It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement). A longitudinal deformation (in the direction of the axis) is called elongation . The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of ...
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Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
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