I am not a carpenter, I am building a blackjack table and am designing the
base and have a question or two about miter(mitre?) cuts.
The frame for the base is going to be built out of 2x4, possible 2x6's.
I need this to be 38 inches in height, but I want the support legs angle in
at about a 30 degree angle. How do I determine the length of the stock that
I need so that retain the height I need?
Compound cuts are next !
Well, not sure how to it mathmatically, but what I would do is miter the
bottom of the leg, mark a level line on wall or something 38" high, hold the
mitered leg next to the wall, mark the height.
When you're doing something like this, then a full-size drawing helps a lot.
A sheet of ply or mdf makes a good surface - opposite sides are parallel,
and the corners are at an accurate 90 degress, so this helps in your layout.
Mark out your stock directly from the drawing.
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first the theory, then a practical answer.
Basic trigonometry gets you there. The 'height' of the angled stock is
the 'sine' of the angle off the _horizontal_, and the distance away from
vertical is the 'cosine' of the angle off horizontal. Note: the 'calculator'
on a Windows PC knows those functions. (under 'view', click 'scientific')
You take the sine of the desired angle (60 degrees, in this case), and
_divide_ the desired height, to get the length of the diagonal.
Now, 30 degrees/60 degrees is a 'special' case. the short side of a 30/60
right triangle is exactly half the length of the diagonal. This makes
the other side "square-root-of-three"/2 of the diagonal. And, conversely,
the diagonal is 2/'square-root-of-three' the vertical distance. square-root-
of-three is 1.732, so half that is .866 Thus, to get a 38" height, you need
a piece that is 38/.866 inches long which works out to a hair over 43-7/8
From your description I can't clearly picture in my sluggish Saturday
morning brain what you need to figure. Some reasonably straightforward
trigonometry will be able to give you the answer, however.
Since I don't have a real helpful suggestion, my point would be that
even after doing the trigonometry, real world conditions are never
what they were supposed to be on paper. Your stock will be somewhat
thinner, thicker, or wider than you intended, your floor isn't flat
and level, your saw's miter gauge is only accurate to 1/2 degree,
etc., etc. (the last being a very important example, since over 38
inches an error of 1/2 degree in that 30 degree angle could become a
I'd suggest leaving the support legs long until they've been fitted or
even attached, and then marking the length and cutting them off.
That's pretty much foolproof, and singularly deals with all the little
inevitable and cumulative errors that occur when working with many
I don't subscribe to the excuse that wood is an amorphous substance
whose dimensions change over time. Although it is true, it is not an
excuse for poor tolerances and sloppy joints. Just the same, no matter
how small your tolerances are when working wood, especially with
angled joints, your materials and equipment will throw you curves, so
it's much better to expect some of them and work with them than it is
to fight them every step of the way...
"Building Your Own Kitchen Cabinets"
With Glory and Passion No Longer in Fashion
The Hero Breaks His Blade. -- Kansas, The Pinnacle, 1975
Cut the miter first, then measure down [along, if on a worktable by
now] and cut the base to length.
I could post a spreadsheet to do any angles/ No of sides, but can't
send binaries here. Where would it go if not here? If needed, state
if you want in degrees, or units of 5 degrees.... [Can do it to
thousandths of a degree for the whackos who post about their refined
saw cuts, but won't.]
I might just send the formula if someone wants to use just that then
OK, I have a better picture of what you mean, but don't know how this
will look at your end:
S ... H
The right side is the height, H
The slope [hypotenuse] S is the length you need.
The angle at the top is 30 deg.
S/H = secant 30deg.
So, S = H*sec(30)
If using a calculator, you won't find that function, so do this:
First make sure you are in degrees, not radians or rads.
Enter 30 then the function Cos, then "=".
Now enter function 1/x "=".
You now have the secant of 30.
Press the multiplication key.
Enter the length H.
Then press '='.
You will have your answer in inches if H was in inches, or cm if H was
Thank you all very much for the information. I have an HP scientific
calculator that i am able to figuire this out on, but in practicality, just
doing it with a full size drawing is going to work best.
Thanks again !
This depends a bit on how you are measuring your 30 degrees. If it is 30
degrees off the horizontal, then the length of the leg sides will be 38
inches times the tangent of 30 degrees. This would get you to the floor.
Unfortunately, I've decided that I can see about a dozen different ways you
might be doing this, and each has a different answer. What you might
consider doing is to draw a cross sectional picture of the table, either
full size or to scale, showing those legs. Make sure you include the
dimensions of the legs, because the answers also vary if you are using
2x4's, 2x6's, or dowels (which would look pretty spiffy), mainly because of
the width of the wood. After you have a good cross section made up, make
the legs to meet the drawing. Note that you also have to consider how the
leg is attached to the frame and the base.
Practicality? Do you have access to a large plotter or are you going to
tape a bunch of pages together? You want 30 degree slant legs to rise 38"?
This is 8th grade stuff.
Oliver had a heap of apples.
Sin = O/H
Cos = A/H
Tan = O/A
To determine the length of the hypotenuse with a side of 38" and an angle
of 60 degrees(which is what I think you mean, not 30, you'd can use sin:
38 = c * sin 60
c = 38/sin 60
c = 43.878
Cut your boards 43-7/8" to the long point of the miter cut and you're
perfect, if I understand your design.
If you really do mean 30 degrees, the boards are going to be 76" long.
76 inches is quite along leg. I'd be concerned of it bending. The
other thing to think about is that these legs might go from a base (of
undetermined height and attachment), to some location presumably under the
38 inches. Oliver and his apples are good once the problem is completely
Measure twice cut once. Measure again, cut again. Measure a third time,
discover that the first cut was right.
On Sat, 17 Apr 2004 21:01:04 GMT, email@example.com (Bruce) wrote:
Another approach in this particular case:
A right triangle with 30,60 other angles has sides in the ratio
1:2:sqrt(3). The 30 deg has to be at the top or the bottom. He
likely means the top, or the table is squat.
In that case, the other non-right angle is 60, at the bottom.
With a vertical side of 38", the slope is twice that divided by
sqrt(3), or 43.88" [ ~43 7/8].
I was just giving an alternate approach, for God's sake. The "rules"
are what makes it work, and they came from an 'understanding' of the
working principles, ratio of sides. It is a matter of understanding,
not of memorising. You learned to do fractions by looking at the
simplest cases first (1/2, 1/3, 1/4, ....) then you learned the rules
you could apply to any other numbers. It's no different here.
In any case, you can figure it out for yourself. I mentioned the
30,60,90 only because it applied in this particular case, as I already
said. That made an easier approach possible. If you stick to just
one method, it's like having just one hammer in your toolbox. You can
ask about each problem as you meet it, or learn the basic principles
and apply them anytime. Your choice.
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