Calculating Angles - Woodworking Talk - Woodworkers Forum
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post #1 of 16 Old 10-29-2015, 10:29 PM Thread Starter
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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
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post #2 of 16 Old 10-29-2015, 10:42 PM
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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....
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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; 10-30-2015 at 12:32 AM. Reason: sp
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post #3 of 16 Old 10-29-2015, 10:43 PM
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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
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post #4 of 16 Old 10-29-2015, 10:44 PM
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.....

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post #5 of 16 Old 10-30-2015, 09:31 AM Thread Starter
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Quote:
Originally Posted by mengtian View Post
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
Well, thanks, guys! That sure muddied things up . This page confused me.

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
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post #6 of 16 Old 10-30-2015, 11:10 AM
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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 tan-1), 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.
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post #7 of 16 Old 10-30-2015, 11:13 AM
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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
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post #8 of 16 Old 10-30-2015, 12:14 PM
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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.

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.
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post #9 of 16 Old 10-30-2015, 12:22 PM
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For some of us it is easier to use math than how to remember how to use a carpenters square LOL
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post #10 of 16 Old 10-30-2015, 12:34 PM
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Quote:
Originally Posted by Hammer1 View Post
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.
I agree with all you said but this. it is not different, the math is being used to calculate exactly that. the angle for cutting the rafter to meet a ridge board would be 26.57 deg, and the cut to sit on the top plate would be 63.43 deg, with the dimensions given.

but I agree the rafter square is the perfect tool for this application.
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post #11 of 16 Old 10-10-2018, 11:19 AM
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Angles-NEWBIE

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.
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post #12 of 16 Old 10-10-2018, 12:34 PM
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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.

A sketch of what you are building would be a big help. I have no idea of what a "leaning shelf unit" is.


George
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post #13 of 16 Old 10-10-2018, 12:54 PM
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A Goggle search turned up this ....



And this which shows the 10 degree cuts:
https://www.familyhandyman.com/woodw...lves/view-all/

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; 10-10-2018 at 12:59 PM.
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post #14 of 16 Old 10-10-2018, 01:17 PM
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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.
It just wouldn't work to go down a parts list cutting and mitering without specific instructions. If the instructions are lacking in info you have to find out where that part goes on the project and how it's used. This is probably the reason the parts list is lacking this info, they expect you to look at the illustration for the application of that part. Then you would know if the miter is on the end or the edge.
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post #15 of 16 Old 10-11-2018, 07:06 AM
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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.
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post #16 of 16 Old 10-11-2018, 02:36 PM
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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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