(CHALLENGING )Trigonometry / geometry proof

AI Thread Summary
The discussion revolves around proving that the length GL equals R(THETA) in a circular structure. A participant suggests that for a circle of radius R, the length of a circular segment corresponding to an angle theta is R theta, which is based on the definition of radians. They explain that if G' is a point on the cylinder, then the arc length G'T also measures R theta. The conversation seeks additional proofs or insights to support this conclusion. Overall, the thread emphasizes the geometric relationship between angles and arc lengths in circular structures.
Doctor_Doom
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(CHALLENGING!)Trigonometry / geometry proof

Hey guys I've spent a couple hours on this without even coming close. I'm hoping someone here can drop me a hint.

From the above image I need to proof that GL is R(THETA) in length. The only other information I have is that GT extended is a type of sheet (metal sheet) balancing and "rocking" forward and backward on the circular structure of radius R (cylinder).

Hints or help or links would be of HUGE assistance.

Thanks in advance!
 
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Is there anything to prove?
If you have a circle of radius R, then a circular segment with angle theta has length R theta.
That's about the definition of radians (a unit circle goes around 2pi radians, and has circumference 2pi).

If you let G' be the marked point on the cylinder below G (near which the label for c is written), then G'T along the circle has length R theta. Since G is a point on the circle with center T which also goes through G' (as indicated by the circular arc), GT is also R theta.
 


Thanks that makes sense. Anyone else have a proof for what was stated above?
 

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