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Topic: Carpenterial angles
Replies: 7   Last Post: Jan 29, 2009 5:56 PM

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Posts: 2
Registered: 5/16/07
Carpenterial angles
Posted: Jan 23, 2009 5:03 PM
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January 23, 2009

How is the math done in the following situation?


You wish to cut down an 8-foot sheet of plywood from 96 inches to
92-5/8 inches. You position the hook of your steel tape measure on
the left end of the sheet so that the top edge of the tape is
everywhere flush with the top of the sheet's edge. You make a pencil
mark at 92-5/8 inches. So far so good.


But what if the steel tape is hooked at the left end correctly but the
right end -- the end where you're going to make a pencil mark at
92-5/8 inches -- is low by 1 inch? I can see that the resulting cut
will be short, but I can't figure out by how much.


Is there a formula? It seems like there should be, but I never took
whatever area of math would teach me this.

Idealized, I think of a circle of radius 1 centered on the X and Y
axes. If I measure from the origin STRAIGHT right 1 unit, the
measurement is correct, but if I measure out 1 unit when the ruler is
erroneously TILTED DOWN a certain distance, the spot I mark will be
short.


Is there a formula that converts this erroneous distance, which
presumably describes an angle, to a calculated distance of error? I
also do understand that the longer is the distance from the origin to
the marked spot, the less the error will be.


Asked perhaps yet another way, as a radius is swept through a circle,
how does the X-axis value shrink as it sweeps from a given y-value to
a smaller one? I think.


Thanks for any light you can shed.

--Johnny


.




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