(CHALLENGING!!)Trigonometry / geometry proof


by Doctor_Doom
Tags: geometry, proof
Doctor_Doom
Doctor_Doom is offline
#1
Mar2-10, 10:16 PM
P: 14
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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CompuChip
CompuChip is offline
#2
Mar3-10, 03:29 AM
Sci Advisor
HW Helper
P: 4,301
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.
Doctor_Doom
Doctor_Doom is offline
#3
Mar3-10, 03:59 AM
P: 14
Thanks that makes sense. Anyone else have a proof for what was stated above?


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