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# a little math ...

Trailboss
Posts: 23079
I'm trying to build a ramp to my trailer. The ramp needs to be 28 and a half inches high. I figure about five feet (60 inches) long from the top of the ramp to the ground.
Using the formula z*z = sqrt( x*x + y*y ) I got
60*60 = sqrt( x*x + 28.5*28.5 ).
Solving for x gave me 52.8.
So the bottom edge is 52.8 inches. The vertical edge is 28.5 inches and the sloped edge is 60 inches. There is a right angle between the bottom edge and the vertical edge.
But I can't remember how to calculate either of the other angles. Anybody know?

Ranch Hand
Posts: 1365
Here are my calculations:

Output (in inches):
Incline length: 60.0
Ground length: 52.799 (more precise)
Ramp height: 28.5
Incline angle: 28.359 (more precise)
Other angle: 61.640 (more precise)
[This message has been edited by David Garland (edited August 25, 2001).]
[This message has been edited by David Garland (edited August 25, 2001).]

paul wheaton
Trailboss
Posts: 23079
Thanks David.
That's so close to 30/60, what would the incline length and horizontal length be if I went with 30 degrees and 60 degrees?

Ranch Hand
Posts: 275
The sine of the acute angle between the ground and the gradient is the ratio between the the gradient(hypotenuse) and the ramp height. Sine of the angle 30 is 0.5 so for a 30 degree angle you would need a one is to two ratio between the ramp height and gradient(hypotenuse).
cheers
PS.If the gradient is 60 inches and the height 30 inches the other side will be
51.961524227066318805823390245176 inches.
Best of luck

[This message has been edited by Sahir Shibley (edited August 26, 2001).]

Ranch Hand
Posts: 316
A 30-60-90 triangle is a "special" triangle having the small side (vertical), long side(distance to door),and hypotenuse (ramp) having a ratio for their respective sides of 1, the square root of 3, and 2.
Sahir has it right, I'm just adding this so you don't have something like "What the heck is a sine?"
Paul R

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