In article <uMnzf.715733$_o.133366@attbi_s71>, 223rem wrote:
>Tomes wrote:
>> "Alan Baker" > wrote in message
>> ...
>>
>>
>>>And the explains the problem:
>>>
>>>" is hard to believe that, after quite literally scaling new heights, he
>>>has just parked his Atlas Grey Audi A6 4.2 quattro 47 metres off the
>>>ground at an angle of 37.5 degrees and that is approximately equivalent
>>>to an 80 percent gradient."
>>>
>>>80%, not 80 degrees.
>>>
>>
>>
>> In a given distance it rises 80% of that distance.
>> Tomes
>
>So how did they get 0.8 from 37.5 degrees?
>Is that the tangent of the slope angle? It is close numerically, but
>it doesnt sound right, as it can exceed 100%. Or is the sinus? That
>doesnt match numerically with 0.8.

Percentage, as written down on the warning traffic signs (e.g.,
http://www.signaco.si/znaki/nevarno/nevar15s.gif and
http://www.signaco.si/znaki/nevarno/nevar16s.gif) is defined as the
vertical distance ascended (or descended) versus the horizontal distance
travelled, 100*b/a in the following diagram:

/|
/ |
c/ |b
/ |
/____|
a

This is the tangens of the angle between sides c and a. The gradient is
also given as 1:X, but this is just the fraction b/a written as 1a/b).

Here's a table of some gradients in degrees and percentages, both rounded
to 0 decimal places:

deg | perc.
===========
90 | infinity
45 | 100
31 | 60
30 | 58
27 | 50
17 | 30
14 | 25
6 | 10

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