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Q: converting slope from percentage to degrees ( Answered ,   0 Comments )
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 Subject: converting slope from percentage to degrees Category: Science > Math Asked by: serendipityseeker-ga List Price: \$2.00 Posted: 14 Nov 2002 18:30 PST Expires: 14 Dec 2002 18:30 PST Question ID: 108034
 ```i need to convert a slope currently expressed as a percentage to degrees. How do i do it ?```
 ```Hello serendipityseeker-ga, Thanks for another math question - my favorite. Slope expressed as a percent means that in 100 feet of horizontal distance, the (road, trail, whatever) has fallen by n%. A little trigonometry will get you degrees. We know that the tangent of an angle is the opposite side divided by the adjacent side. The arctangent then gives the angle when you give it the opposite / adjacent fraction. Draw your triangle like this (I hope the ASCII art comes through) |\ A | \ | \ |______\ B C That looks to me to be about a 100% grade (100 feet out, 100 feet down). Label the two sides of the triangle as A and B, and the angle we are considering is C. arctan(A/B) = C. Fix B to be 100 feet, and then A is the percent grade. If you have a 10% grade, then you compute the angle C as arctan(10/100) = 5.7106 degrees. If you have a 100% grade, then we see the formula works: arctan(100/100) = 45. If you want the other angle, you use a bit of geometry. First off, we have fixed thet bottom left angle to be 90 degrees, and we know the sum of the angles in a triangle is 180. Therefore, the top angle is 90 - C degrees (180 degrees total - 90 degrees in bottom left angle - C. I simplified.) FYI: arctan is also called the inverse tangent, and is written as tan^-1 (with the exponent formatted better!). -Haversian```
 serendipityseeker-ga rated this answer: `almost to complicated for a math dummy like me...but i got there. thanks very much.`