table problem

Johnny357

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Jun 12, 2005
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I have a table who's top is 36.75 in. wide, I want the table to be 30 in. tall but, I want the legs to be crossed how do I find the length of the table legs keep in mind that the leg is a 2X4 and i also need to find the angle of the cut to keep the leg flush anginst the table. The 2X4 is actully 1 7/8X3 3/4.[/url]
 
Johnny357 said:
I have a table who's top is 36.75 in. wide, I want the table to be 30 in. tall but, I want the legs to be crossed how do I find the length of the table legs keep in mind that the leg is a 2X4 and i also need to find the angle of the cut to keep the leg flush anginst the table. The 2X4 is actully 1 7/8X3 3/4.
I'm going to assume that we don't care about the 1+7/8 side of the 2x4, since you're going to place the legs with the 3¾ side vertical, right? Also, the legs won't be sticking out, right? This is for a REAL table, right? If it's a homework assignment, I'd give an entirely different answer.

The figure I imagine is a parallelogram. It has small horizontal edges and much longer diagonal edges. One horizontal edge is against the bottom of the table top and the other horizontal edge is on the ground.

The first chunk of information is easy. It's just the Pythagorean Theorem:

30"<sup>2</sup> + 36.75"<sup>2</sup> = Z<sup>2</sup>, where Z is the diagonal between the two most distant corners, the edge of the table on one side and the ground on the other side.

Z = 47.4401" = apprx (47 + 14/32)" -- Just a hair more

With a little work, it can be determined that the angle you need to cut is 43.7595º. If you can cut that angle and measure the 47.4401", you're done.

If you can't cut that angle, you'll have to measure something else.
1) Suffice it to say that you'll need a piece of lumber 44.4755" = apprx (44 + 15/32)" -- a little bit more.
2) From the GROUND end of the board, along the TOP edge, measure 3.9160" = apprx (3 + 29/32)" -- a bit more, actually.
3) From that point, construct a perpendicular to the bottom edge.
4) You should be able to measure from the point on the bottom edge back to where you started, a distance of 5.4220" = apprx (5 + 13/32) -- again, a little more. Make this cut after checking your measurements 12 times. :)
5) Do the same thing on the TABLE end, but start on the BOTTOM edge, constructing the perpendicular to the top edge.

I rounded to 1/32" and ignored the width of the saw blade. Your carpentry skills will have to compensate for those two items.
 
Whoops! I forgot the thickness of the table top. The solution above puts the BOTTOM of the table at 30". Would you like a new version, or can you adjust for that? If you would like a new version, you'll have to supply the thickness - 2x4s again? Then we could use the (1 + 7/8)".
 
Thanks for your help :D, but could you please explain the other theorems you used to find the angles of the cut, I do understand the Pythagorean Theorem but I would like to understand the others so I can do this later without bothering you. Could you also show me a drawing of the figure.

Thanks, Johnny357
 
Oh, you don't ask for much. :wink:

These applications are used:

-- Pythagorean Theorem (the whole leg)
-- Definition of Tangent (the whole leg)
-- Pythagorean Theorem (the cut piece)
-- Definition of Tangent (the cut piece)
-- Similar Triangles (cut piece vs. whole leg)

I hope you can read it. I'm not very skilled at this particular software. This version is shortened to make room for the table top inside your 30".

http://img193.echo.cx/img193/5420/tableleg0rq.gif

If you sell over 100,000 units, you owe me royalties! :lol:
 
See what you've done! Now you've got me thinking about it.

The design, as rendered, probably is of little value. Those sharp corners will hurt someone. I think most designs lop off 3/4" or so to blunt them.

You could just chop, leaving a little margin around the edge of the table, or recalculate with a slightly larger board and a slightly sharper angle.
 
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