Calculate angle from drawing - Woodworking Talk - Woodworkers Forum
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Old 06-27-2020, 04:22 PM Thread Starter
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Calculate angle from drawing

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.
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Old 06-27-2020, 05:08 PM
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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.
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Old 06-27-2020, 05:39 PM Thread Starter
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Well, "trig out" is a term that is over my head LOL
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Old 06-27-2020, 06:09 PM
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Originally Posted by RichO View Post
Well, "trig out" is a term that is over my head LOL
"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
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Old 06-27-2020, 06:22 PM
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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.
Set the protractor on the base or bottom edge and read the angle.
No math required.

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; 06-27-2020 at 06:56 PM.
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Old 06-27-2020, 06:36 PM
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Originally Posted by woodnthings View Post
You can always make a layout on your bench top and just measure the angle with a digital angle finder or a protractor:

No math required.
Yep that what he's doing now, yet he asked about the math.
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Old 06-28-2020, 01:25 AM
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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.
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Old 06-28-2020, 01:48 AM Thread Starter
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Originally Posted by Dave McCann View Post
"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
I do understand that part of it. It becomes a triangle with one 6" side, one 28" side and one 90 degree angle. Using the Pythagorean theorem, the hypotenuse is 28.635". So, using those figures, how did you come up with 77.9 degrees for the angle?
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Old 06-28-2020, 01:50 AM Thread Starter
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Originally Posted by Dave McCann View Post
Yep that what he's doing now, yet he asked about the math.
Yes, just figured a few numbers punched into a calculator would be a quicker method. Correct me if I am wrong :)
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Old 06-28-2020, 03:05 AM
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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
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Old 06-28-2020, 08:34 AM
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Originally Posted by RichO View Post
I do understand that part of it. It becomes a triangle with one 6" side, one 28" side and one 90 degree angle. Using the Pythagorean theorem, the hypotenuse is 28.635". So, using those figures, how did you come up with 77.9 degrees for the angle?
Basic Formulas.
sin θ = Opposite Side/Hypotenuse.
sec θ = Hypotenuse/Adjacent Side.
cos θ = Adjacent Side/Hypotenuse.
tan θ = Opposite Side/Adjacent Side.
cosec θ = Hypotenuse/Opposite Side.
cot θ = Adjacent Side/Opposite Side.

Knowing the length of two sides is all that is needed to get the angle shown in your example.

Now days, you don't even need to know the formula, just use an online calculator such as this; https://www.calculator.net/right-tri...alculator.html

You know the lengths of sides (a) 6 inch and (b) 28 inch, just plug in the values and hit calculate. You don't need to know the length of all three sides all you need is any two sides.
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Old 06-28-2020, 09:31 AM
where's my table saw?

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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.

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)
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Old 06-28-2020, 09:46 AM Thread Starter
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Great. That calculator is perfect. Thanks!
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Old 06-28-2020, 01:57 PM
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Originally Posted by woodnthings View Post
but the math doesn't lie.
it rarely does

i'm an engineer by education.
i believe i'm a credit or 2 short of a math degree, as are most engineers
nobody memorizes trig formulas except before a trig test
i'd google an online calculator like dave did
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Old 06-28-2020, 02:54 PM
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nobody does not what?

sin=opposite/hypotenuse
tan=sin/cos

that and a 'scientific' calculator with inverse sin/cos/tan and no internet is required.
and before calculators, there was the CRC Handbook - which I still have....
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Old 06-28-2020, 03:18 PM
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Originally Posted by TomCT2 View Post
nobody does not what?

sin=opposite/hypotenuse
tan=sin/cos

that and a 'scientific' calculator with inverse sin/cos/tan and no internet is required.
and before calculators, there was the CRC Handbook - which I still have....
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.
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Old 06-28-2020, 11:28 PM
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As promised...excuse my crappy handwriting
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Old 06-29-2020, 07:55 AM
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ya'll lost me way back at "then, you pick up the protractor" - - - - -

.

there is no educational alternative to having a front row seat in the School of Hard Knocks.
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Old 06-29-2020, 10:03 AM
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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.

-----Dave

Last edited by HoytC; 06-29-2020 at 10:07 AM.
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Old 06-29-2020, 11:08 AM
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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.
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