(CHALLENGING )Trigonometry / geometry proof

  1. (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: Mar 3, 2010
  2. jcsd
  3. CompuChip

    CompuChip 4,299
    Science Advisor
    Homework Helper

    Re: (CHALLENGING!!)Trigonometry / geometry proof

    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.
     
  4. Re: (CHALLENGING!!)Trigonometry / geometry proof

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