Slope and Translation

SLOPE AND TRANSLATION:- Positive Gradient or Elevation Home
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Parameters Distance AB Distance BC
Default Values 20 15
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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 ø = tan-1(BC/AB).

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

TEST YOUR UNDERSTANDING: Find a suitable slope i.e. path or driveway then using a piece of string calculate the gradient positive Or negative. Providing the slope is reasonably linear then doing this over a short distance will suffice. Which you then scale up.

Remember you are not measuring the length of the slope; unless you want to of course then it's the hypotenuse of the resulting triangle. You might need to use a stick and spirit level to establish a true height.

The gradient of a slope is measurement of the incline when the level reached Is 47.99cm over a distance of 1.44m. Calculate the gradient. Choose Answer option: A = 0.42 | B = 0.37 | C = 0.17 | D = 0.33