Woodworking Talk banner

Calculate angle from drawing

8K views 37 replies 16 participants last post by  TimPa 
#1 ·
At the cabinet shop I work at, we build compound mitered wood hoods for many homes. While there are different ways to build one, the guy that heads my department draws it out full scale on a sheet of wood and then uses a digital protractor to get the correct angle to cut the pieces at.

I am not much of a geometry guy but there must be some kind of formula you can use to get the angle based on the measurements, like in the attached drawing.

I searched google for finding the angles in a trapezoid but the only results I am getting are based on the other angles, not the measurements. Looking to find the angle at the red arrow.

Thanks for the help.
 

Attachments

See less See more
1
#2 ·
The angle in question is 77.9 degrees for the example shown. Keeping in mind that the information given is only enough to calculate the simple angle shown, not a compound angle. To figure the angles as in the example, simply "remove" the 24 by 28 rectangle in the center and trig out the angles of each right angle triangle on each end.
 
#4 ·
"Trigonometry," is the basis for all calculations of a right triangle. Something which will serve you well if you will be working with simple and compound angles.

Right triangle
A right triangle is a type of triangle that has one angle that measures 90°. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry.
In a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse. The sides of a right triangle are commonly referred to with the variables a, b, and c, where c is the hypotenuse and a and b are the lengths of the shorter sides. Their angles are also typically referred to using the capitalized letter corresponding to the side length: angle A for side a, angle B for side b, and angle C (for a right triangle this will be 90°) for side c
 
#5 · (Edited)
When trig is too much .....

You can always make a layout on your bench top and just measure the angle with a digital angle finder or a protractor:





In this case, subtract 24 from 36 and get 12. Strike a vertical line using a drywall square from the edge of your bench and make a tick mark at 28" up.

Move over 6" at the base (because 6 is 1/2 of 12 and you have 2 sides or angled pieces), and make a tick mark.
Connect the marks.
That's your angle.
Set the protractor on the base or bottom edge and read the angle.
No math required. :surprise2:
 
  • Like
Reactions: TobyC and bargoon
#7 ·
You need to find the angles in order for the formulas to work but yes they do exist...find a calculator that can do both sin/cos/tan as well as their inverses. I'll post the formulas for compound miters later when I'm less sleep deprived. Remember sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
 
#10 ·
I would draw a triangle that is 28" high , 6" at the base. Connect the two and this gives you the angle needed.
6" is half the distance from 36"-24"=12", divide in half and it is 6". Transfer the angle to a bevel square. Then to your saw. I made a large bevel square from scrap maple that is 18" long . This would make the angle set more accurate .
mike
 
#12 ·
hypotenuse length ?

If the adjacent side is 28", the base is 6" the calculator says that "c" is only 28.6". That intuitively seems a bit short to me, but the math doesn't lie. :|
 
#16 · (Edited)
The most used item from my drafting tools is,,,,,,,,,,,,,,,,,,,,,,,,,, my eraser shield! And don't forget a slide rule for doing the calculations.
Drafting machine? That was only for the guys with seniority, the rest of us used a tee square and triangles. I imagine there are plenty of folks who have never seen or come across either item.
 

Attachments

#19 · (Edited)
I don't think any of the calculations so far shown are correct. There's simply not enough information to calculate that angle. OP implied that the figure is a trapezoid but did not say that it is an isosceles trapezoid, which is what it appears that everyone is assuming. If that's a template made at a jobsite I don't think it's safe to assume anything about it. Just measure it.


Of course if it is isosceles then the angle is obviously the inverse tangent of 28/6 like several people have said.
 
  • Like
Reactions: TobyC
#20 ·
I have never gotten over how much I use math for woodworking, especially geometry, geometric construction, and trigonometry.

... so much so, that I keep a scientific calculator and a small precision drafting set (two compasses and a divider) in the garage.

The slide rule lives in my desk. I don't use it any more, but I can't bear to part with it.

I was truly blessed to have great math teachers when I was young. Somehow, someway, they made it stick. By now, they are all gone, but they did their jobs well, and they cared.
 
#21 ·
At the risk of showing my age, here is the calculator from my university days. As you can see it has all the trig stuff anyone would ever need. I quite enjoy all the math involved in woodworking, but I don't do any with the slide rule, now it's all done with my trusty HP 11C and 15C. Can't beat RPN.
 

Attachments

#30 ·
I'm not going to pretend to know squat about mathematics, but at least I didn't look at a business card that has "carpentry" printed on it then ask, "Oh! So you do carpets?"
That actually happened to my son yesterday.. lol

"Carpet builder!"
 
#31 ·
They make compound wood hoods .....

At the cabinet shop I work at, we build compound mitered wood hoods for many homes. While there are different ways to build one, the guy that heads my department draws it out full scale on a sheet of wood and then uses a digital protractor to get the correct angle to cut the pieces at.

I am not much of a geometry guy but there must be some kind of formula you can use to get the angle based on the measurements, like in the attached drawing.

I searched google for finding the angles in a trapezoid but the only results I am getting are based on the other angles, not the measurements. Looking to find the angle at the red arrow.

Thanks for the help.
hoyt is correct, we are assuming that the cabinet maker is construcing a symmetrical hood. but the formulaes provided are for the resulting angle, not the "compound" angle you referred in the op.

here is a good website for the compound angle calculation:


http://www.pdxtex.com/canoe/compound.htm
It was duly noted in post #2 that the answer given was for a simple angle NOT a compound angle.

So, which is it, compound or straight/vertical sided hood? The angle won't change in the view that was first posted, BUT If the sides are not vertical it will lean away from vertical and the angle will change slightly, at least that's what my intuition tells me. :|
Probably the best way to do this is via Sketch Up, which I don't know how to use ...... where you enter the height, length and width values and it will calculate all the angles.


The title was misleading:
Calculate angle from drawing

"Calculate" implies using math.

"from the drawing" could mean either using math or a constructed

diagram with just measurements.
If the angles are compound, then I would use the online calculator.
:vs_cool:
 
#32 ·
Assuming this is an isosceles trapezoid (symmetrical), using the height to find the angle in the triangle at the bottom right, 77.91 degrees. Subtract from 90 to find the angle at the top of the triangle. As the angle adjacent to this is a right angle, add 90 to get the obtuse angle of the top of the trapezoid.
 

Attachments

#33 ·
I do have a follow up question regarding one online angle calculator someone posted a link to.

I just built a compound hood this week using this page to come up with the angle. However, I am puzzled by what they are referring to with the "End Angle". I was expecting that to be 90 minus the slope angle (21.801) which is the angle I used to bevel the top and bottom of the "box", but what angle or cut is the 20.374 supposed to apply to? Any ideas?

Thanks
 

Attachments

#34 ·
The end angle can be ......

The end can be at angle you choose from straight up vertical to the same as the sides depending on your hood design. Most of the online calulators I've (not used) have the same angle on the ends as on the sides making the compound cuts identical. It would certainly throw a slight "curve" (not really) in the equation if the end angle is different. do ask me what to do in that case. I have made similar objects including a roof for a wishing well with 8 sides just by a "cut and fit" method after establishing the height. I then set the fence on the jointer to make the joint more precise. FYI, I enjoy math but was never much good at it. I flunked analytic geometry in college and that was a 5 credit course ..... :sad2:
 
#37 · (Edited)
Correction/edit ....

The end can be at angle you choose from straight up vertical to the same as the sides depending on your hood design. Most of the online calculators I've (not used) have the same angle on the ends as on the sides making the compound cuts identical. It would certainly throw a slight "curve" (not really) in the equation if the end angle is different. DO NOT me what to do in that case. I have made similar objects including a roof for a wishing well with 8 sides just by a "cut and fit" method after establishing the height. I then set the fence on the jointer to make the joint more precise. FYI, I enjoy math but was never much good at it. I flunked analytic geometry in college and that was a 5 credit course ..... :sad2:

Corrected wrong info.....
 
#36 · (Edited)
That was my original though but that angle should be 21.8 degrees, always 90 minus the slope of the hypotenuse.

woodnthings, I get what you are saying, and personally I prefer to slightly adjust the angles of the horizontal ends as to get a nice tight fit at the top and bottom joints. It's just that this calculator seems to be based on geometric calculations to achieve a specific end result so that is where the 20.374 is confusing.
 
This is an older thread, you may not receive a response, and could be reviving an old thread. Please consider creating a new thread.
Top