(CHALLENGING )Trigonometry / geometry proof

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SUMMARY

The discussion focuses on proving that the length of segment GL is equal to R(THETA), where R represents the radius of a circular structure and THETA is the angle in radians. The proof utilizes the definition of radians, stating that a circular segment with angle THETA has a length of R(THETA). The participants clarify that for a circle of radius R, the arc length can be derived from the relationship between the angle and the radius, confirming that both segments GT and G'T along the circular path measure R(THETA).

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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!
 
Last edited:
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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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