Does 30% of inclination mean the triple of 10%?

First of all we will have to mathematically define the meaning of inclination. Those who have already studied geometry know that the inclination of a straight line can be measured through the angle it forms with the positive semi-x axes. But if we are driving and we see a traffic sign showing the road has an ascent of inclination of 10%, what does that mean? To simplify things it is enough to think that for each 100 metres we horizontally drive, the road vertically “ascended” 10 metres, that is, in terms of altitude, we are 10 metres above the starting point.

And how many degrees does an inclination of 10% correspond to?

Coming back to the initial definition, let’s calculate the angle of the road inclination. If we think about a rectangle triangle in which one of its cathetus measures 100 metres and the other measures 10 metres, we are able to determine the angle degree of the road inclination by using trigonometry. In this case a calculator having the tangent function tells us that that the inclination of 10% corresponds to an inclination of 5.71º.

And what about an inclination of 30%?

Using trigonometry once more we are going to think about a rectangle triangle in which one of the cathetus measures 100 metres and the other measures 30 metres. In this case the inclination corresponds to 16.7º. in conclusion, to answer the question that led us to these calculations, we can easily check that `5.71 xx 3 != 16.7`. So, a road with 30% of inclination does not correspond to the triple of another one whose inclination is 10%! Therefore we can guess that a road with 20% of inclination is not twice the inclination of one with 10% of inclination.

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