I am older and I've not messed with Trig/Geometry in quite some time. I have a problem I need help solving.
I have a cone with circumference "X"/diameter "X1" at the bottom and a height of "Y". I have to wrap a "T" high collar all the way around this cone at different heights "H" from the bottom (or top).
I know the values for X, X1, Y, H and T. What I need to figure out is: 1) "C", the bottom circumference of my collar at height "H" up the cone from the bottom, 2) "A1", the angle of the cone surface from bottom to top (predicated, I assume, on the change in circumference over distance "H") and finally, 3) from "A1", figure "A2", the arc of the collar in order for it to lie flat against the surface of the cone as it's placed over the cone (without an arc, the collar will point straight up from wherever it sits on the cone like a crown sitting on your head. I need the collar to lie slanted inward towards the center of the cone so that it lies flat against the cone's surface, which requires the collar to be arc shaped, based on the value of A1 (I think)).
Obviously, the math is a bit out of my league. What I'm looking for is an equation into which I can plug my known values and get my unknowns.
See the attached illustration.
Thanks in advance for any help.
I have a cone with circumference "X"/diameter "X1" at the bottom and a height of "Y". I have to wrap a "T" high collar all the way around this cone at different heights "H" from the bottom (or top).
I know the values for X, X1, Y, H and T. What I need to figure out is: 1) "C", the bottom circumference of my collar at height "H" up the cone from the bottom, 2) "A1", the angle of the cone surface from bottom to top (predicated, I assume, on the change in circumference over distance "H") and finally, 3) from "A1", figure "A2", the arc of the collar in order for it to lie flat against the surface of the cone as it's placed over the cone (without an arc, the collar will point straight up from wherever it sits on the cone like a crown sitting on your head. I need the collar to lie slanted inward towards the center of the cone so that it lies flat against the cone's surface, which requires the collar to be arc shaped, based on the value of A1 (I think)).
Obviously, the math is a bit out of my league. What I'm looking for is an equation into which I can plug my known values and get my unknowns.
See the attached illustration.
Thanks in advance for any help.
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