Tigerbiten
Guru
I think it goes like this.
10% = 1/10. or "one in ten" so altitude increases by one unit for every 10 units of road. So, using Pythagoras' Theorem, there is a right-angled triangle whose Opposite side (O) is 1, the Hypotenuse (H) is 10 and the Aajacent side (A) is the square root of 99 (10 squared minus 1 squared).
The sine of the angle of slope of the road is O/H. In this case sin (slope) is 0.1, so the slope is 5.7 degrees
Not quite correct.
A 1-in-10 is for every 10 units you go horizontal, you go up 1 unit vertical.
So you are working with O/A, which is the tan of the angle not the sine.
At low angles the difference is small, so an 11.5 degree slope is still a 20% hill.
But as the angle grow, the difference increases, a 30 degree slope is a 57% hill not 50%
and a 45 degree slope (a 1-in-1) is a 100% hill, not a 70% one.