Carpenterial angles
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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
.
K. E. Pledger
> 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.
If I understand you aright, you're concerned that the sheet may not have exact right angles at the corners. Is that it?
If so, you need your tape to be perpendicular to the left or right edge, rather than "everywhere flush with the top" edge. Have you a T-square (or even a very large try-square) to do that accurately? If not, there are other tricks for making right angles, so post again if you don't know any.
HTH
Ken Pledger.
JohnnyG
Ken,
I appreciate your response but no, that's not at all what I'm getting
at. Please read my entire original post.
--Johnny
Joshua Zucker
> K. E. Pledger wrote:
>> > 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.
It's just a Pythagorean theorem problem: the hypotenuse is 92 5/8
inches and one leg is 1 inch and the other leg is what you actually
measure.
For practical purposes, probably unmeasurably small difference ...
something like .006 inches I think?
--Joshua Zucker
JohnnyG
=============
January 29, 2009
Cheers, Joshua Zucker and all,
Thanks, Joshua, for taking an interest.
Is the triangle you're imagining truly a right triangle?
If it is then can you define the three points in terms of X and Y
coordinates or some other way so I can see what you're seeing? As I
see it now, one of the X-axis measurements is at 92-5/8 and the other
-- the cock-eyed one -- is at some distance less than that along the X-
axis, which would mean it's not a right triangle, wouldn't it?
If the triangle you imagine is not a right triangle, is it still true
that "It's just a Pythagorean theorem problem"?
As I asked a previous respondent, are you sure you read my entire OP?
I look forward to your reply.
--Johnny
JohnnyG
Cheers, Joshua Zucker and all,
Thanks, Joshua, for taking an interest.
Is the triangle you're imagining truly a right triangle?
If it is then can you define the three points in terms of X and Y
coordinates or some other way so I can see what you're seeing? As I see it
now, one of the X-axis measurements is at 92-5/8 and the other -- the
cock-eyed one -- is at some distance less than that along the X-axis, which
would mean it's not a right triangle, wouldn't it?
If the triangle you imagine is not a right triangle, is it still true that
"It's just a Pythagorean theorem problem"?
As I asked a previous respondent, are you sure you read my entire OP?
I look forward to your reply.
--Johnny
http://barelybad.com
Joshua Zucker
> If it is then can you define the three points in terms of X and Y
> coordinates or some other way so I can see what you're seeing? As I see it
> now, one of the X-axis measurements is at 92-5/8 and the other -- the
> cock-eyed one -- is at some distance less than that along the X-axis, which
> would mean it's not a right triangle, wouldn't it?
No, the 92 5/8 inch is not along the x-axis - you said that the end of
the tape measure has dropped one inch below the x-axis, correct? If
the 92 5/8 was along the x-axis, then there wouldn't be any problem,
you'd have the measurement you want.
Thus the 92 5/8 is the hypotenuse of the triangle, the one inch is the
y coordinate, and the x coordinate can be found by the Pythagorean
theorem.
If I'm misunderstanding you, then I think you better draw a picture of
what you actually mean.
--Joshua Zucker
K. E. Pledger
> I appreciate your response but no, that's not at all what I'm getting at.
Please don't assume that I didn't. Both Joshua Tucker and I have tried to understand you, but failed.
How about labelling the four vertices A, B, C, D and giving a fresh description? Are you confident that there are reliable right angles at the corners? Are you confident that the opposite sides are reliably parallel? What exactly are you measuring with your tape?
Ken Pledger.