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.