Mathematics Principles V11

Clive W. Humphris

SLOPE and TRANSLATION: Positive Gradient or Elevation. 


The gradient or slope of a line is found by dividing the vertical distance (height) by the horizontal distance travelled. The angle is often referred to as the angle of elevation (sloping upward from the horizontal) or the angle of depression (sloping download from the horizontal).

The slope of a hill for example will have a gradient of say, 1 in 5, which if expressed as a ratio is 1 : 5. It could be necessary to determine the height of a mast, which is a positive elevation from the ground when the horizontal distance is known and the angle of elevation can be found using a simple pointer. Then applying of the trigonometric ratio will return the height.

Upward slopes will have positive gradient or elevation whereas downward are negative. The angle of the gradient can be determined by the application of trigonometry. The angle ΓΈ = tan-1(BC/AB).

Horizontal distance is also sometimes known as run, and the vertical as rise.


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