I have a known object's edge length, and a set degree between them (1-10).
How can I calculate my possible Radius given a constant length and given degree offset?
Even if my fixed length + fixed degree = greater or less than a 360 degree circle.
My priority is determining the closest radius either slightly over or under 360/180/90.
This equation will help me rapidly recommend a degree of curvature given a varying client's radius.
Example Constants:
- Video wall panel with a known length (landscape or portrait) 1214mm x 683mm
- 10 options of degrees ranging from 1 to 10 - only a single degree may be used per calc.
If Segment/Chord/Facet Length is 683mm and degree is 7° - what is my radius?
The inverse, I think, would solve for how many [683mm] segments can fit within a given radius at varying degrees?
I hope this is clear enough - I'm kind of in a spot where I don't know what else to ask but I feel there is a "segments of a length within a given arc/circle" equation I'm unaware of.
I can do this in 3D and get my answers but wish I knew the math too. Please and Thank you in advanced and may 42 be with you.
-E²
See attached for contextual application - complete circles are unlikely if not impossible
If I understand your problem correctly, you want to construct a regular polygon using fixed length panels. The number of sides (i.e., the number of panels) depends on the degree offset (lets call the offset $d$). Given that in a regular polygon the interior angles are given by $\frac{180(n-2)}{n}$, where $n$ stands for the number of sides, you need to solve $$\frac{180(n-2)}{n}=180-d\implies n=\frac{360}{d}$$In your $7º$ example, you'd need $360/7$ panels, a little more than $51$ panels in order to make a full circle.
As for the radius, you need to compute the the apothem, i.e., the distance from the side of your polygon to the center. This can be done using the formula $$\frac{a}{2\tan \frac{\pi}{n}},$$ where $a$ is the fixed length of your panel. In your example with $a=683$ and $d=7$, the radius would be $$\frac{683}{2\tan \frac{7\pi}{360}}\approx5583.48.$$ Note that I've used the exact ($\frac{360}{d}$) rather than the approximate ($51$) number of sides.