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angle to percent grade

angle to percent grade
by kim on 06/07/04 at 06:53:44

My high school trig has failed me.  how do you convert an angle in degrees to a percent grade (as on a highway - 10 % grade)?

we recently were on the Mount Washington Cog Railway - the second steepest in the world at a 39 degree incline.  i believe that a 45 degree incline is a 100 percent grade but cannot figure out how to arrive at the correct grade for a 39 degree incline.

thanks!

Kim

Re: angle to percent grade
by Robert Fogt on 06/07/04 at 17:23:23

The slope is the Tangent of the angle.

Slope is rise/run, and the % grade is 100 times the slope. So a slope of 1/1 would be a 100% grade, which is indeed a 45 degree angle.

So if you know the degree of the angle, just enter it into your scientific calculator then hit Tangent.

The Tangent of 39 degree angle is:
0.809784

That is the slope, now multiply by 100 to get the % grade.
80.9784 %

Re: angle to percent grade
by Kim Pollock on 06/08/04 at 10:41:48

Thanks Robert -

I missed the part about multiplying by 100 - mystery solved!

Kim P

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