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Mega Tree Re-calculation


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I'm hoping there is a math wiz out there that can answer this....


I have a Mega Tree from CLS.  Because my front yard slopes downward, I have changed it so that the 20 foot center pole goes into a 2' hole in the ground instead of using the base as designed by CLS.  This allows the tree to stand straight up.


I am also using the PVC frame (as designed by CLS) for the bottom of the tree.  Since this sits on the ground, the base kind of follows the contour of the ground.

I want to modify the base so that there is only a bottom ring suspended from the center pole of the mega tree, and eliminate the rest of the framework.


My bottom ring is currently 40 inches above the ground.  The radius at this point is 5 feet.


So the tree is 18' (216 inches) tall with the bottom ring 40 inches above the ground.  This makes the trunk 176 inches.  The radius is 5' (60 inches).


I would like to lower the bottom ring to 20" above ground level, but maintain the same angle of the light strings.  This would make the trunk length 196 inches.


I am familiar with the Pythagorean therum (A squared + B Squared = C Squared).  Since the length of both C and B are both changing, I can't apply it in this case.


My question is what should the radius of the bottom ring be -- to lower it 20 inches but maintain the same angle of the light strings? 





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Similar triangles' (triangles having the same angles)  dimensions are proportionally the same. Thus,


x/196 = 60/176


x/196 = .340909...


x = (196)(.340909..)


x = 66.8181...

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