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Calculating Angles
Hi Everyone,
I don't know the formula for determining angle cuts. I home one of you more experienced woodworkers can help me.
If you will look at the attached drawing (I can't draw and I misspelled angle), but you can figure it out.
Is all the info you need included in the drawing? I know there are TWO different angles necessary. I also need to know formula.
Thanks in advance for your help.
Regards, Jim
I don't know the formula for determining angle cuts. I home one of you more experienced woodworkers can help me.
If you will look at the attached drawing (I can't draw and I misspelled angle), but you can figure it out.
Is all the info you need included in the drawing? I know there are TWO different angles necessary. I also need to know formula.
Thanks in advance for your help.
Regards, Jim
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use a tangent calculator
The tangent of a right triangle is the side opposite divided by the side adjacent in decimals.
Your base is 3.5 and your height is 7.0. The calculator shows a 63 degree and 27 degree angles:
http://www.mathopenref.com/trigtangent.html
just drag the right side point or vertex, to 3.5 and drop the height to 7.0 and you will see....
Your base is 3.5 and your height is 7.0. The calculator shows a 63 degree and 27 degree angles:
http://www.mathopenref.com/trigtangent.html
just drag the right side point or vertex, to 3.5 and drop the height to 7.0 and you will see....
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
Last edited by woodnthings; 10302015 at 12:32 AM. Reason: sp
http://www.csgnetwork.com/righttricalc.html
You have two right triangles with the center (7') splitting them. The other length for each side is 3.5 (7/2). The angles would be:
63.43 and 26.57
You have two right triangles with the center (7') splitting them. The other length for each side is 3.5 (7/2). The angles would be:
63.43 and 26.57
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.....
Last edited by Sorrowful Jones; 10292015 at 10:54 PM.
Quote:
Originally Posted by mengtian
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http://www.csgnetwork.com/righttricalc.html
You have two right triangles with the center (7') splitting them. The other length for each side is 3.5 (7/2). The angles would be:
63.43 and 26.57
You have two right triangles with the center (7') splitting them. The other length for each side is 3.5 (7/2). The angles would be:
63.43 and 26.57
http://www.csgnetwork.com/righttricalc.html
If I did it correctly, the angles would be 54 & 36. I used 7 and 5 as my a & b.
=================
Side a
7
Units Of Length
Side b
5
Units Of Length
Side c
9
Units Of Length
Angle A or B
54
Degrees
Angle C
90
Degrees
Angle 3
36
Degrees
====================
It still ISN'T correct..........or I'm using the wrong chart. What the heck is ANGLE 3? It doesn't show up in the graphic.
Formulas mess up my mind .
I'm going back to that 2nd link I was referred to and see if I can make heads or tails of it.
Thanks, Jim
Senior Member
That web site is pretty confusing references to "angle A or B" and "angle 3" are very misleading, to say the least.
As others have said, the tangent is "side opposite over [divided by] side adjacent, or, as carpenters would say "rise over run". Then you need to find the arctangent (arctan or tan1), which is the angle has the tangent you calculated (typically the "2nd" function button on a lot of handheld calculators).
If you mentally rotate the triangle so the dashed line is the run, and the rise is half of the width, your tangent is 3.5'/7', or 0.5. The arctan of 0.5 is ~26.6 degrees. Since the peak consists of two triangles, the cut angle at the peak is actually 53.1 degrees (~26.6 x 2).
The cut angle at the right side is not 63.4 degrees; that is the angle inside the triangle. For the correct angle cut, you need to add 90 degrees (from the rectangular section below the triangle), so the cut at the angle on the right side of your diagram is 153.4 degrees.
As others have said, the tangent is "side opposite over [divided by] side adjacent, or, as carpenters would say "rise over run". Then you need to find the arctangent (arctan or tan1), which is the angle has the tangent you calculated (typically the "2nd" function button on a lot of handheld calculators).
If you mentally rotate the triangle so the dashed line is the run, and the rise is half of the width, your tangent is 3.5'/7', or 0.5. The arctan of 0.5 is ~26.6 degrees. Since the peak consists of two triangles, the cut angle at the peak is actually 53.1 degrees (~26.6 x 2).
The cut angle at the right side is not 63.4 degrees; that is the angle inside the triangle. For the correct angle cut, you need to add 90 degrees (from the rectangular section below the triangle), so the cut at the angle on the right side of your diagram is 153.4 degrees.
Angle 3 is either A or B. If you use 63.43 (63) as angle A then Angle 3 is your Angle B.
90  63.43 = 26.57
90  63.43 = 26.57
Senior Member
People are giving you mathematical solutions to finding the angles of the triangle, however, you are probably looking for the angles to cut boards that will meet in the center of the peak. Similar to cutting rafters on a house. This is entirely different, you want to bisect the peak angle not cut what it is in total.
This is simple with a carpenter's framing square. These are the large squares with a 16" leg and a 24" leg. Divide the 7' width by 2, = 3.5'. Use either the two outside edges or the two inside edges of the square, don't use outside on one and inside on the other. Align the 3.5" mark on the short edge of the square with the bottom edge of the board and align the 7" mark on the long edge of the square, same edge of the board. Draw a line on the long edge, this is the bisect cut for the peak, (plumb cut). Now, make a mark along the short edge of the square, this is the level, (seat) cut at the bottom of the board. It can help with visualization if you choose the top edge of the board you want to use and hold it roughly on the angle you want in front of you as though you are looking on the end of the triangle. It will be easy to see that you need a plumb cut and a seat cut and how those relate to the square and the board. Be careful with some framing squares, one edge might be marked in 10ths or metric, use the edges with inch marks.
This is simple with a carpenter's framing square. These are the large squares with a 16" leg and a 24" leg. Divide the 7' width by 2, = 3.5'. Use either the two outside edges or the two inside edges of the square, don't use outside on one and inside on the other. Align the 3.5" mark on the short edge of the square with the bottom edge of the board and align the 7" mark on the long edge of the square, same edge of the board. Draw a line on the long edge, this is the bisect cut for the peak, (plumb cut). Now, make a mark along the short edge of the square, this is the level, (seat) cut at the bottom of the board. It can help with visualization if you choose the top edge of the board you want to use and hold it roughly on the angle you want in front of you as though you are looking on the end of the triangle. It will be easy to see that you need a plumb cut and a seat cut and how those relate to the square and the board. Be careful with some framing squares, one edge might be marked in 10ths or metric, use the edges with inch marks.
For some of us it is easier to use math than how to remember how to use a carpenters square LOL
Senior Member
Quote:
Originally Posted by Hammer1
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People are giving you mathematical solutions to finding the angles of the triangle, however, you are probably looking for the angles to cut boards that will meet in the center of the peak. Similar to cutting rafters on a house. This is entirely different, you want to bisect the peak angle not cut what it is in total.
but I agree the rafter square is the perfect tool for this application.
Junior Member
AnglesNEWBIE
Ok. I am an absolute newbie and feel really stupid for this question but I am tired of chopping up wood and finding that I have no clue. Here is my question. My wife and I would like to build a leaning shelf unit. Every plan I see gives us what would seem to be easy instructions of "cut each end at a 10 degree angle. If I am looking at the 2x4 (for example) is the 10 degree measured from the top of the board or the side? Also when I thought I had it right, two 10 degree angles would make the legs come out about 12 feet from the wall so it didn't seem like making them the same made sense. Shouldn't they be 10 and 80 degrees? Help a simpleton out if you can.
Senior Member
Quote:
Originally Posted by Ted Strong
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Ok. I am an absolute newbie and feel really stupid for this question but I am tired of chopping up wood and finding that I have no clue. Here is my question. My wife and I would like to build a leaning shelf unit. Every plan I see gives us what would seem to be easy instructions of "cut each end at a 10 degree angle. If I am looking at the 2x4 (for example) is the 10 degree measured from the top of the board or the side? Also when I thought I had it right, two 10 degree angles would make the legs come out about 12 feet from the wall so it didn't seem like making them the same made sense. Shouldn't they be 10 and 80 degrees? Help a simpleton out if you can.
A sketch of what you are building would be a big help. I have no idea of what a "leaning shelf unit" is.
George
A Goggle search turned up this ....
And this which shows the 10 degree cuts:
https://www.familyhandyman.com/woodw...lves/viewall/
See it that helps.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
Last edited by woodnthings; 10102018 at 12:59 PM.
Senior Member
Quote:
Originally Posted by Ted Strong
View Post
Ok. I am an absolute newbie and feel really stupid for this question but I am tired of chopping up wood and finding that I have no clue. Here is my question. My wife and I would like to build a leaning shelf unit. Every plan I see gives us what would seem to be easy instructions of "cut each end at a 10 degree angle. If I am looking at the 2x4 (for example) is the 10 degree measured from the top of the board or the side? Also when I thought I had it right, two 10 degree angles would make the legs come out about 12 feet from the wall so it didn't seem like making them the same made sense. Shouldn't they be 10 and 80 degrees? Help a simpleton out if you can.
Senior Member
the "10 degree" angle actually refers to a 10 degree angle off of the typical 90 degree that the ends are cut to, in reference to the face and the edge. on your miter saw it may say 10 degrees or 80 degrees. but it is 10 degrees off of perpendicular or 90 degrees.
some terminology
board face: the 3 1/2" surface of a 2" x 4", board edge: the 1 1/2" surface running along the length of the board, and the end is obviously the surface we typically off, end.
I believe that your 10 degrees (80 degrees) is in reference to the edge.
some terminology
board face: the 3 1/2" surface of a 2" x 4", board edge: the 1 1/2" surface running along the length of the board, and the end is obviously the surface we typically off, end.
I believe that your 10 degrees (80 degrees) is in reference to the edge.
Junior Member
Thanks to all for the insight and answers. I have been looking for a forum like this. Hopefully in time I will be able to contribute vs ask for help. ;)
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