Silly Question About Right Triangles and Cutting Wood - Page 1
Forum section: electronics / general

author: bostonman
author_rank: Super Contributor
timestamp: November 25, 2024, 03:11:26 am
content: This may sound silly, but I'm confused about reference points regarding a "right triangle" and cutting the angles for wood on a saw.I've been in the process of building a fence. I installed the fence posts (4" x 4"s) and installed the horizontal pieces (2" x 4"s). At a certain point the fence had to have a slight rise so I had to cut the 2" x 4"s ends at an angle.Attached is a picture of the section. The left shows the example, and the right is the same, but includes dimensions (I used several decimal places rather than the risk of confusion over rounding).The confusion I had is my saw goes from 0 to 45 degrees. When I drew the right triangle referencing it to one vertical point, I got the (correct) 5 degrees and began questioning why I need to change reference points on the other end because it needed the same 5 degree cut to make the angle.After I began sending my brain into a spiral by wondering why it's not 85 degrees, so I questioned when to reference it to one point versus the other.Why do the reference points at each end change and why is it not 85 degrees?Obviously I know trig and angles, but going from a right triangle on paper to a piece of wood on a fence suddenly got confusing.

author: Kean
author_rank: Unknown
timestamp: November 25, 2024, 03:30:20 am
content: The saw is normally cutting at 90 degrees when it is set to 0 degrees.So a setting of 5 degrees will offset from 90 and give corner angles of 85 and 95 degrees.Rotate the stock to swap the angles for the other end.

author: bostonman
author_rank: Super Contributor
timestamp: November 25, 2024, 03:54:18 am
content: Is it cutting at 90 degrees with respect to the fence on the saw (the horizontal rest) or 0 degrees with respect to the saw blade?Either way, when looking at the wood fence in regards to a right triangle, but ends can't be 5 degrees (or 85 degrees), so the reference angles change.This is the confusion I'm having. If I didn't imagine the horizontal 2" x 4"s laid horizontally, mathematically I would have assume one end gets cut at 5 degrees and the other end 85 degrees.

author: Kean
author_rank: Unknown
timestamp: November 25, 2024, 04:07:44 am
content: Quote from: bostonman on November 25, 2024, 03:54:18 amUm... yes? Or 270 degrees, or 180 degrees... depends on what you are referring to and your measuring reference...Quote from: bostonman on November 25, 2024, 03:54:18 amI would say they are 90 degrees +/- 5 degrees = 85 & 95 degrees. Again, it depends on what plane you are referencing against.

author: bostonman
author_rank: Super Contributor
timestamp: November 26, 2024, 04:01:13 am
content: QuoteI fully agree and understood this from start, but the planes change and it can cause great confusion. Had I not looked at the fence, or mentally visualized it (along with looking at how the saw would cut the wood), I would have cut one end at 5 degrees and the other at 85 degrees (assuming my saw rotates beyond 45 degrees).Instead, one end of the wood needs to be cut 5 degrees based on plane A, and then the other end also needs to be 5 degrees based on plane B. So one needs to "just know" to switch planes.

author: zapta
author_rank: Super Contributor
timestamp: November 27, 2024, 01:38:21 pm
content: I am cunfused about the confusion. The board has 85 and 95 degrees corners on the right and 95 and 85 corners on the left. To cut them you need 5 and -5 degrees on the saw or just 5 degrees and then same 5 degrees with the board flipped

author: bostonman
author_rank: Super Contributor
timestamp: November 28, 2024, 12:34:50 am
content: QuoteThe confusion is from having to switch planes to accommodate the angle.If this was purely a right triangle, I'd tell you to cut one side is 5 degrees and the other 85. This isn't the case, both ends of the board are 5 degrees.When I go to the saw thinking the angle is say 85 degrees or 95 degrees, I have to look and see my options are only 0-45 degrees and say: well, the angle must be 5 degrees since my saw doesn't cut angles that high.So my confusion isn't 95 degrees is the same as 5 degrees, my confusion is: I have to switch how the (imaginary) right triangle is positioned to "calculate" both ends are 5 degrees per my original drawing I included.

author: jpanhalt
author_rank: Super Contributor
timestamp: November 28, 2024, 02:16:32 am
content: The more said here, the more the picture gets confusing. A sketch would help. Are you using a table saw, radial arm saw, or a related chop saw?In cases where I have to fit a board like it sounds, I set the angle at 5° and flip the board for the other end. That way, if the miter is off a little, at least they are the same or complements depending on how you describe it.

author: bostonman
author_rank: Super Contributor
timestamp: November 28, 2024, 04:04:35 am
content: I provided a sketch in my initial post.As for the saw, it's a compound mitre saw (the base rotates +/- 45 degrees and the arm tilts from vertical to 45 degrees; a double (?) compound mitre saw tilts +/-45 degrees which mine isn't.

author: IanB
author_rank: Super Contributor
timestamp: November 28, 2024, 05:49:19 am
content: Your apparent confusion remains very difficult to understand.You simply set the saw to a 5 degree angle and cut each end of the horizontal pieces to that same angle, being careful to get the orientation correct for each cut. Marking the position of the cuts with a pencil before cutting helps to avoid making mistakes.More difficult than the angle would be getting the length right, which would be about 3/8 inch longer than the 88 inch horizontal between posts.

author: 5U4GB
author_rank: Super Contributor
timestamp: November 28, 2024, 06:16:36 am
content: Quote from: Kean on November 25, 2024, 03:30:20 amYou can also get mitre-saw protractors that help with this, google "mitre protractor", they take all (well, most) of the "have I got this right in my head" problem of getting the angles the right way round away. Woodpeckers probably have an exotic but also quite expensive one but I'm quite happy with my $10 Aliexpress model.

author: jpanhalt
author_rank: Super Contributor
timestamp: November 28, 2024, 09:55:32 am
content: Quote from: bostonman on November 28, 2024, 04:04:35 amSorry, I missed that link. A compound miter saw is like a radial arm saw, that is, you don't usually move the wood.Assuming the long side is against the fence your setting is 5°. Make one cut. Then depending on your outrun table or space you can either flip the board and leave the miter the same, or set the miter 5° in the other direction and re-position the board accordingly to get parallel cuts.

author: 5U4GB
author_rank: Super Contributor
timestamp: November 29, 2024, 10:49:01 am
content: Quote from: Uno Plast on November 29, 2024, 10:32:17 amAnd in particular if you've never done it so far, square your saw. There's a ton of posts and videos on doing this, e.g.and.Mitre saws have an amazing ability to move themselves half a degree out of square when you're not looking, so always check with an angle that you're starting off square.Quote from: Uno Plast on November 29, 2024, 10:32:17 amAnd never, ever put your hand inside the marked zone on the saw to hold a small piece that you're cutting. The lines mark the zones in which your fingers will be pulled into the saw blade if the piece catches and gets pulled in... if you want to do it properly, google "ten million dollar stick", or alternatively use a zero clearance fence or similar.

author: bostonman
author_rank: Super Contributor
timestamp: December 01, 2024, 01:44:17 pm
content: Thanks for the videos.Unfortunately the adjustments on my saw are different, but the concepts are still applicable.I'm probably just overthinking the angles. As stated, having to mentally change reference planes to accommodate both ends being 5 degrees (unlike a right triangle that's 5 and 85 degrees) caused confusion. Had I not tinkered with practice cuts, and saw the saw only goes 0-45 degrees, I would have assumed one side needed to be 5 degrees and the other side 85 (or 95) degrees.

author: Kean
author_rank: Unknown
timestamp: December 01, 2024, 02:06:17 pm
content: Quote from: bostonman on December 01, 2024, 01:44:17 pmLook again at the sketch you drew, and where the red arrows point.The 5 degree angle you keep referencing is the tight angle measured between the lower face of the sloping rail and the horizontal plane (i.e. at right angles to the vertical posts). This reference plane does not exist on the cut timber.The 85 degree angle is measured from the upper face of the sloping rail to the vertical post. This is a 90 degree right angle minus the 5 degree slope.The (unmarked) 95 degree angle would be between the lower face of the sloping rail to the vertical post. This is a 90 degree right angle plus the 5 degree slope.As mentioned, your saw cuts at right angles from the fence (saw fence, not property fence), so the 0-45 degree mitre setting is an offset (+/-) from 90 degrees.

author: IanB
author_rank: Super Contributor
timestamp: December 01, 2024, 09:17:55 pm
content: Quote from: bostonman on December 01, 2024, 01:44:17 pmYou don't need to mentally change reference planes. You drew a diagram. From the diagram, it is obvious that both ends have the same 5 degree angle to the vertical. Why do you keep bringing up right triangles? There is a long, horizontal piece of wood with a slant to it. If the slant is 5 degrees, then the ends will also be at 5 degrees to the vertical.You drew the diagram and calculated the 5 degrees. You now transfer the diagram to the wood, mark where the 5 degree cuts go, and cut them. Keep the saw locked in the same position for all cuts, to make sure they all line up properly at the fence posts.

author: bostonman
author_rank: Super Contributor
timestamp: December 02, 2024, 02:04:43 pm
content: I'm only bringing up "right triangles" because that's how I visualized the initial problem and look at it overall.The cuts have been completed weeks ago, but prior to cutting, I remember doing a quick calculation and saying: one side will be at a 5 degree angle and the other will be at 85 degrees. After I looked at the saw and realized it went 0-45 and thought: I can't make one end 5 and the other 85, so the reference planes need to be swapped so both ends are 5 degrees, but why.Then I cut a sample piece of scrap wood and realized both ends are 5 degrees.On a side note, as expected, the calculated and actual 5 degrees wasn't accurate. Due to posts not being 100% vertical and/or any warping, I had to experiment a bit with the angles so the cuts didn't have spaces.

author: timeandfrequency
author_rank: Frequent Contributor
timestamp: December 02, 2024, 03:19:27 pm
content: hello bostonman,Yes, for most miter saws, the scale is centered around 0°, so you can setup positive and negative angles.And when the rotating table (or tiltable fence) is on the '0°' mark, the blade is actually at right angle (= 90 °) vs the fence.For your work, you need to set + 5° and - 5° (or always keep +5°and flip the part, as other members mentionned above).Make a try with a scrap part to see how it goes.For your cuts, as you already know the values of the angles (with little adjustment), you do not even need any 'miter protractor' (also called 'angle finder') (jump to 1:01 time mark).@5U4GB 1st video is great : clever idea to use a magnetic digital angle gauge to ajust the vertical angle exactly to 90° (video at 3:55 time mark)

author: bostonman
author_rank: Super Contributor
timestamp: December 02, 2024, 11:35:05 pm
content: Thanks for the video. I have something similar to that, but what's the fun if you can't apply math to the problem.The angle finder is cool. I have one, but I don't know the sensitivity or the accuracy. I think it's a cheap one that only provides a rough angle and not ideal for calibrating when tiny increments are needed.Funny, earlier I was thinking about an incident when I was younger, I had a project that needed wood cut (this was before I knew anything about angles on saws and had only cut wood with a hand saw). I applied trig and gave the angles (and dimensions) to my father to cut the wood. When I told him, he said it can't be that angle, it's too large (or small).Long story short, he drew a picture on the basement floor (it's still there today) and started to realize that if he subtracted the number I gave him from 90, then the angle was more realistic to cut on a saw.I'm only providing this story because it goes back to a statement I made: had I not used a practice piece of wood, saw the scale on the saw only goes from 0-45, or visualized the actual angle, I would have assumed the angle needed to be 85 degrees.

author: jpanhalt
author_rank: Super Contributor
timestamp: December 03, 2024, 12:47:40 am
content: Let me offer an alternative. First, your drawing imples the fence boards are a little less than 3" wide (i.e, 8-5 =3, but that's the hypotenuse of a 5° triangle). That's a odd size, so I assumed 3-1/2" (i.e, a 2x4). If the boards are really something else, I will redo the calculation.1) Carefully unplug your miter saw and put it in storage.2) Take your board and using your steel rule, make a mark88.306"88.669" from the left end on the edge nearest you. Call that the bottom edge. Draw a vertical line to the opposite (top) edge.3) Measure exactly 0.306" in from the bottom edge on the left end, and 0.306" to the left on the top edge at the previously made vertical line at the other end.4) Using your straight edge, connect the left end mark to the upper left corner of the board.5) On the right end of the board, draw a line from the top mark to the bottom of the vertical on the same end.6) Get a framing saw (hand is safer) and cut at the lines two angled lines you just drew.You should now have your board with parallel ends at 5° to the cord that will span 88" horizontal (88.363 " on the angle)EDIT: Misread the original drawing and corrected for the horizontal distance v. slant distance. Directions corrected.Attachment: