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Nedd help with geometry!!(10 posts)

Nedd help with geometry!!Len J
May 22, 2001 9:28 AM
I'm embarrased to ask this, but does anyone remember how to calculate the angle of rise of a hill when you know the distance of the hill and the elevation change? I've lost my high school geometry book.
lots of formulas...dave
May 22, 2001 1:29 PM
Assuming by the "distance of the hill", you mean the longest side of the triangle (hypotenuse), the sine of angle is the rise (elevation change) divided by the hypotenuse. The tangent of the angle is the rise divided by the horizontal run. The % grade is tangent of the angle mutiplied by 100. Then there's the handy formula: A squared times B squared equals C squared, where C is the hypotenuse. Confused yet?

Keep in mind that hills are seldom straight. More often they're curves that produce an ever-changing grade.
lots of formulas...Len J
May 22, 2001 1:33 PM
True, but I was really looking for an average grade.
lots of formulas...Len J
May 22, 2001 1:33 PM
Any chance of saying this in english?
Problem isn't your language, it's my understanding "nm"Len J
May 22, 2001 1:38 PM
Easy mathJonathan Zook
May 22, 2001 2:05 PM

The equation you are looking for is really quite simple. Grade is the percentage of rise relative to run, or elevation gained/horizontal distance traveled. Since the horizontal distance is not known, you will use the Pythagorean Theorem of squaring the sides of a triangle (a2 + b2 = c2) to calculate this. b is elevation gained, c is distance traveled on the climb, and a is the unknown horizontal distance. So in effect you'll adjust the equation to be a2 = c2 - b2. Then a = the square root of c2 - b2. Once you have calculated the horizontal distance, then grade will be simply b/a. The resulting grade will be an average for the whole climb.

For more triangle geometry, you can check out:

Hope this helps!!
Easy mathLen J
May 22, 2001 2:08 PM
re: Nedd help with geometry!!Wayne
May 23, 2001 1:50 PM
Here is the formula:

Grade (x) = elev gained x 100 divided by distance traveled in feet

Ex What is the grade of a climb of 264 feet in 1 mile
Answer 5%

x = 264 x 100 =26400 divided by 5280 = 5%
May 23, 2001 9:21 PM
I'm not a math major but 26400 divided by 5280 is equal to 5 not 5%.
264 is 5% of 5820.
I think,
% Grade = elevation gained divided by distances traveled (measured in equal units)

Who is Nedd, and why is he so good at geometry? (nm)MeDotOrg
May 23, 2001 9:41 PM