Figuring how to mark an angle....help

[Dennis Peacock]

I'm trying to figure out how to mark a 22.5 degree angle on a desktop that is 4' wide by 5' long. Is there an equation or rule of thumb that I can do to figure out the layout lines for 22.5 degrees? Let's say that I have one side that is 35.5" long and at one end of that, I need to mark a 22.5 degree angle away from that line. What is the distance from the starting point out to give me my 3rd point?

I'm asking because I don't know. :)

[Clint Baxter]

According to my construction calculator, a run of 35.5” and 22.5 degrees leaves a rise of 14.7”

if the rise is 35.5, the run will be 85.8”

Clint

[Pat Barry]

If you, for example, were to measure 20 inches along the baseline then across 20 inches at a 90 degree angle, connecting the resulting point with the starting point would create a 45 degree angle. If instead you went only 10 inches across from the same 20 invh mark on the baseline you would create a 22.5 degree angle. So for 35.5 inches, half that, or 17.75 would give you 22.5 degrees.

[Jeff Heath]

Another option, without any math at all, is bisecting the 90° first, and then bisecting the 45° angle left over. All you need to do that is a drafting compass. Takes less than 60 seconds. No math.

[Floyd Mah]

The correct solution can be gotten by simple trigonometry.

The definition of a tangent of an angle is the length of the opposite leg of a right triangle divided by the length of the adjacent (non-hypotenuse) leg. In this case, the angle is 22.5 degrees and the adjacent leg is 35.5 inches.
tan(22.5 degrees) is 0.41421356237 per the google calculator.
35.5 x tan(22.5 degrees) is 14.705 inches.

Before you accept any of these answers, you need to understand the calculations involved. One of the comments above would give you an answer that is off by enough to give you trouble.

[Prashun Patel]

Pat, are you sure that is correct?

I just had to do something like this yesterday. I set my table saw miter gauge to the correct angle and then placed it upside down on my panel. Then I held up a straight edge to the fence and traced the projected line. No math.

[Jim Morgan]

If you, for example, were to measure 20 inches along the baseline then across 20 inches at a 90 degree angle, connecting the resulting point with the starting point would create a 45 degree angle. If instead you went only 10 inches across from the same 20 invh mark on the baseline you would create a 22.5 degree angle. So for 35.5 inches, half that, or 17.75 would give you 22.5 degrees.

No, you would end up with an angle of 26.6°. Trigonometric functions are not linear.

[Dennis Peacock]

Thank you all! I was just trying to figure out how I could simply measure with a bit of math on larger panels and be fairly accurate before making the cut.

[Jacob Reverb]

Handy bookmark:

Trig Calculator
http://www.carbidedepot.com/formulas-trigright.asp

What I like about it is that you don't have to jack around with sin, cos, tan, Oscar had a heap of apples stuff -- you just fill in the blanks on a triangle and it gives you the info you need.

And since it's based on Java or Javascript or whatever, if you save the web page, you can use it even if you don't have an Internet connection.

[Ken Kortge]

I'm not sure if this will help, but ...

Using the Law of Cosines for not necessarily right triangle (using Excel formula format):

Opposite = SQRT(Adjacent1^2 + Adjacent2^2 - 2*Adjacent1*Adjacent2*COS(RADIAN(Angle)))


Angle = DEGREES(ACOS((Adjacent1^2 + Adjacent1^2 - Opposite^2)/(2*Adjacent1*Adjacent2)))


Where Angle is the angle between the two Adjacent sides - given in degrees.
Where Adjacent1, Adjacent2, and Opposite are the lengths of the respective sides of the non-right triangle.

Ken K.

P.S. - If it helps, here are formulas (using Excel format) for right triangles (I suspect you can use the same format for Google Drive Spreadsheets):

Using Right Triangle Trigonometric Functions (Sin, Tan, Cos, ...):
Opposite = Hypotenuse*SIN(RADIANS(Angle))
Opposite = Adjacent*TAN(RADIANS(Angle))
Adjacent = Hypotenuse*COS(Radians(Angle))
Adjacent = Opposite/TAN((RADIANS(Angle))
Hypotenuse = Adjacent/COS(RADIANS(Angle))
Hypotenuse = Opposite/SIN(RADIANS(Angle))
Angle = DEGREES(ASIN(Opposite/Hypotenuse))
Angle = DEGREES(ACOS(Adjacent/Hypotenuse))
Angle = DEGREES(ATAN(Opposite/Adjacent))

[Pat Barry]

No, you would end up with an angle of 26.6°. Trigonometric functions are not linear.

My bad. Sorry for the miscalculation.

[Zachary Hoyt]

I have one of those cheap clear plastic protractors like you used to use in school hanging on the wall in the shop, and very occasionally I'll use it. It's pretty fast and reasonably accurate, though a bigger one would be better for the size of job you are doing.
Zach

[Tim Bueler]

A rafter book will have a page for 22.5* if you have one of those handy. I often used a rafter book even after I got my first Construction Master calculator. For many cuts it was faster to look it up in the book.

[Derek Cohen]

Basic stuff ....

Mark a 45 degree line using a mitre square ( such as a combination square ... everyone has one?). Run this line and the baseline each for, say, 8", and then join them. The centre of this line, and back to the starting point, is 22.5 degrees. Take you less time to do than write this!

Regards from Perth

Derek

[Edwin Santos]

If you wanted to avoid the math, you could take two straight sticks of your chosen length cut on your table saw or whatever. Join them at the end with a machine bolt and wing nut.
You now have a long shop made bevel gauge.
Set it to 22.5 degrees using your method of choice and tighten it down at this setting. Your reference could be a simple protractor, bevel guide, a piece of stock cut at 22.5 on your miter saw (if you trust it), or using a compass to bisect 90 degrees twice or some other reference.
Now strike your line where you want it.
Having a good quality locking bevel gauge is a useful thing to have. Lee Valley used to make a great one that the discontinued. Shinwa makes some very nice stainless steel ones. Of course there will be cheapies at HD or Lowes.

[Jim Morgan]

Basic stuff ....

Mark a 45 degree line using a mitre square ( such as a combination square ... everyone has one?). Run this line and the baseline each for, say, 8", and then join them. The centre of this line, and back to the starting point, is 22.5 degrees. Take you less time to do than write this!

Regards from Perth

Derek

Like Pat Berry's formula in #3 above, this is incorrect. The resulting angle would be about 26.6°. Again, trigonometric functions are not linear.

At 8", a 22.5° angle requires a rise of about 3 5/16", not 4".

If you were to draw an 8" arc from the end of the baseline to the end of the 45° diagonal, a 22.5° line would bisect the arc. But that is not the same as bisecting the straight line drawn between the two endpoints.

[Gary Ragatz]

Handy bookmark:

What I like about it is that you don't have to jack around with sin, cos, tan, Oscar had a heap of apples stuff --

When I was in high school, it was SOH-CAH-TOA - I like the "Oscar ..." bit, but I'd probably forget which order they're in! :)

[Prashun Patel]

Derek is not saying the same thing as Pat. This method would work.

He's not using the sides of a triangle, he's bisecting a sector of a circle. Blah blah blah. Dead horse, beaten

[Floyd Mah]

Derek is correct. He created two identical right triangles that fit inside the isosceles triangle with the 8" sides. Half of the 45 degrees is 22.5 degrees.

This whole discussion reminds me of the story of the math teacher who gives a protractor to his students and asks them to measure the height of a tall building. Many correct solutions, but none of them using the protractor and math tables.

[Jacob Reverb]

Basic stuff ....

Mark a 45 degree line using a mitre square ( such as a combination square ... everyone has one?). Run this line and the baseline each for, say, 8", and then join them. The centre of this line, and back to the starting point, is 22.5 degrees. Take you less time to do than write this!

Regards from Perth

Derek

Derek - I'm not following what you mean when you say "...and then join them." Could you elaborate for my feeble mind? I'm always up for learning simpler ways to do stuff.

[Gary Ragatz]

Derek - I'm not following what you mean when you say "...and then join them." Could you elaborate for my feeble mind? I'm always up for learning simpler ways to do stuff.

Maybe a picture - you can bisect any angle this way:

401123

[Jacob Reverb]

Thanks, Gary. For some reason the "and join them" was throwing me. I was trying to "join" the lines rather than their endpoints.

[Rich Engelhardt]

Thank you all! I was just trying to figure out how I could simply measure with a bit of math on larger panels and be fairly accurate before making the cut. I just use my 12" digital protractor, set to 22.5 degrees, to layout about a foot long line on the panel, then place my track saw track on the line and cut it.

That's my simplified math method.

The only time consuming part is taking the cover off and sticking the battery in the protractor, then taking the battery back out for storage.

Makita and Festool both make a protractor attachment for the track saws that just slips on the track that are mechanical and require no battery, but, as far as I can tell - neither has a 22.5 degree or 45 degree stop, so a protractor is still required for setup.

I don't wish to sidetrack the thread - but - so many people have the attitude that track saws are just for breaking down sheet goods, I like to point out how simple they can make other tasks.

[roger wiegand]

Using a compass and straightedge to bisect the angle will produce a more accurate result, quickly, and with no error prone calculation math or measurements. It works for any angle.

401245

[steven c newman]

Real problem: Desk sides.
401395
Bad matching angles.....two pieces of scrap wood =
401396
Laid one over the other, make a cut ( or three) until things line up..
401397
To cut this, I used a batten, and a circular saw...
401402
Once I get the top, and the lid ready....I'll report back as to what angles were cut...

401403401404401405
Trying to build a sit-down version of this desk. Patterned after Underhill's Rachel's Standing Desk..

[Derek Cohen]

Steven, simply use a sliding bevel gauge. You can gauge the centre by eye, and the rule off both sides. Plane to the lines.

Regards from Perth

Derek

[steven c newman]

Getting set up..
401507
Might be a couple days....scrap block seems to be easier to hang on to....