# Geometry sucks!



## Hamberg (Aug 28, 2021)

Good at math but geometry eludes me - algebra, no issues; figuring out a mitre angle, and I'm on the floor in a fetial position crying !

My go-to method has always been trial and error - little cuts until the joint works. But there has to be a better way?? Some, super secret, carpenter only method that is only accessible via some sort of industry handshake??

Example below (from a deck railing I was installing yesterday) - could someone (anyone) please explain an *EASY* way to figure the angle(s) needed to make this joint?


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## havasu (Aug 28, 2021)

Is that 90 degree location an outside wall? What are you trying to achieve? Sometimes crooked walls are just part of doing business, but the straight line should be aesthetically pleasing to the eye. The way your drawing shows, the ?? area is also 90 degrees.


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## Eddie_T (Aug 28, 2021)

Here's a link to an article on miter angles but it can make it more confusing.

Miter Angles and Miter Saws | THISisCarpentry


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## Snoonyb (Aug 28, 2021)

Or, simply square cut and add something like these; decorative wood post top blocks


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## Hamberg (Aug 28, 2021)

havasu said:


> Is that 90 degree location an outside wall? What are you trying to achieve? Sometimes crooked walls are just part of doing business, but the straight line should be aesthetically pleasing to the eye. The way your drawing shows, the ?? area is also 90 degrees.



Hey @havasu for example purposes, the 90 is an out side wall. The railing was on a (concrete) porch and was far from square. Although, without the railing, cosmetically it looked fine. 

Here is a more exaggerated example of what I'm talking about - assume the ?? lines followed the porch footprint, how would the two mitre angles be calculated?


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## Hamberg (Aug 28, 2021)

Eddie_T said:


> Miter Angles and Miter Saws | THISisCarpentry



That (article) is exactly why I'd be laying on the floor crying


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## Snoonyb (Aug 28, 2021)

If they point where the ?? are, isn't, 90 degrees, then set a speed square on one side and the degree of difference will be revealed. Divide the difference in two and that's the degree of adjustment for the cut.


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## Hamberg (Aug 28, 2021)

Not finished, and I'll get a couple pics of the railing top next week when I finish, but here are a few pics of the project.


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## havasu (Aug 28, 2021)

All 4 corners of a square will equal 360 degrees. Using a adjustable T square, you find that angle, then the remaining angle will need to add up to 360 degrees. But as said earlier, you just need to have the project aesthetically pleasing to the eye, so "wing it!"


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## Hamberg (Aug 28, 2021)

havasu said:


> All 4 corners of a square will equal 360 degrees.



Right but what happens if it isn't a square, do they still add up to 360°? Is this illustration correct?


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## havasu (Aug 28, 2021)

Then you would have an oblique angle.
"The definition of an oblique angle is *one that is not 90 degrees*. ... An angle, such as an acute or obtuse angle, that is not a right angle or a multiple of a right angle."
I would have to pull out my geometry books for that.

However, in the pic above, your unknown would by 92 degrees. Hell, you got my brain smoking now.


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## Eddie_T (Aug 28, 2021)




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## Spicoli43 (Aug 29, 2021)

I hate Math so much that after reading this, I have no idea what you want to do. When I need an angled cut, I guess and use a scrap piece until I get the cut exactly right.


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## havasu (Aug 29, 2021)

Nothing wrong with making a cardboard pattern. Many granite counter installers hot glue furring strips to the exact angles needed, and they come out perfect and best of all, no math is needed.


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## Eddie_T (Aug 29, 2021)

I have traced an angle onto paper then folded to bisect the angle.


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## zannej (Aug 29, 2021)

All I'm remembering is Pythagorean's theorum and my Sikh geometry teacher saying "Right angles are congruent" in an Indian accent...


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## mabloodhound (Aug 29, 2021)

In your example, only the top railing needs to have the miter angle cut.  Take two pieces of the material you will use for the top rail, cut slightly longer than needed.  Then lay one on top of the other in the position they are going to be and mark both sides of the top board onto the bottom one.  Then reverse the boards putting the other one on top and mark both sides on the other one.  Now draw a line from the inside corner of the marked line to the outside corner om both boards.  This is the angle to cut.


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## Hamberg (Aug 30, 2021)

Eddie_T said:


>




@Eddie_T - *EXACTLY *what I was looking for!!! thanks!!


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## Hamberg (Aug 30, 2021)

Spicoli43 said:


> I hate Math so much that after reading this, I have no idea what you want to do. When I need an angled cut, I guess and use a scrap piece until I get the cut exactly right.



@Spicoli43 - HAHAHA exactly what I do now!!! Just looking to not waste any more wood (or time :O))


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## Eddie_T (Aug 30, 2021)

Just a thought, use the video technique to mark and cut the first rail then with the rails in place trace a line on the second rail. BTW it's looking good!

Here's another trick for an inside miter;


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## Hamberg (Aug 31, 2021)

used the trial-fit method :O) to finish this one.
But next one...


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## Eddie_T (Aug 31, 2021)

Nice workmanship!

When using woodworking tricks it's always good to understand why the trick works. The ones shown for bisecting the angle are actually intersecting parallel lines (equidistant from the legs of the angle) represented by the straight and parallel edges of the boards.


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## 68bucks (Aug 31, 2021)

Here's how I would calculate that angle. Measure from the corner of the house to the corner of the railing. Measure the other legs of the triangles and then apply trig functions to calculate the angles. I think I've seen some online calculators too.
Of course in real life I'd probably make a pattern or something similar.


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## Eddie_T (Aug 31, 2021)

68bucks said:


> Here's how I would calculate that angle. Measure from the corner of the house to the corner of the railing. Measure the other legs of the triangles and then apply trig functions to calculate the angles. I think I've seen some online calculators too.
> Of course in real life I'd probably make a pattern or something similar.


A triangle with a 92° angle doesn't readily lend itself to the trig functions.


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## Hamberg (Aug 31, 2021)

I started out saying I had "ISSUES" with geometry and now you're talking trigonometry...


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## zannej (Aug 31, 2021)

Thanks for the videos, Eddie. Those were helpful.
Now if I can find a super easy way to figure out the angle of a slope for pipe drop/rise.


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## Eddie_T (Aug 31, 2021)

@Hamberg If your willing to tackle faux stone painting or veneering the foundation of that porch could be transformed. I have a friend that painted faux brick on a Florida concrete block stucco house. He was experienced in graphic arts though.


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## Hamberg (Aug 31, 2021)

zannej said:


> Now if I can find a super easy way to figure out the angle of a slope for pipe drop/rise.



Hey @zannej have you seen Hammerpedia's 1/4 bubble trick?


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## Eddie_T (Aug 31, 2021)

My 2' level doesn't have  ¼ bubble marks so I would tape a ½" block on one end.


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## 68bucks (Aug 31, 2021)

This might help. 




__





						Triangle Calculator
					

This free triangle calculator computes the edges, angles, area, height, perimeter, median, as well as other values and a diagram of the resulting triangle.




					www.calculator.net


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## Eddie_T (Aug 31, 2021)

I thought of a method using a 45° triangle and a straight edge that could work with some precise measurement and the use of trigonometric functions. However the direct no measurement bisection would probably be more accurate.


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## Hamberg (Sep 1, 2021)

68bucks said:


> This might help.
> 
> 
> 
> ...



YUP, clear as mud!!


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## zannej (Sep 1, 2021)

Thanks! Dylan really is cool. One of these days I will subscribe to something. I actually saw another pretty cool trick someone used. He wanted his pipe to slope 1" over 4ft so he added a 1 inch block to the end of his level to raise it up so it would show as level when the pipe dropped 1". I've also seen they have torpedo levels with an adjustable part you can spin so that it will show as level when you have it at a specific slope. So if you find that 1/4" per foot slope and rotate the part you can use that one to tell when something is sloped properly.


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## Eddie_T (Sep 3, 2021)

I didn't think to try to work a sine bar into this discussion, and don't think I will.


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## Hamberg (Sep 4, 2021)

I would not try to cut that square with your table saw - just sayin'  

(also, your hypotenuse is showing :O/)


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## bud16415 (Sep 5, 2021)

Eddie_T said:


> I didn't think to try to work a sine bar into this discussion, and don't think I will.


Being trained as a tool and die maker and spending 43 years around the industry I thought I had seen every kind of sine bar ever made. But I your wooden one is something new to me. Very cleaver.


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## Eddie_T (Sep 5, 2021)

bud16415 said:


> Being trained as a tool and die maker and spending 43 years around the industry I thought I had seen every kind of sine bar ever made. But I your wooden one is something new to me. Very cleaver.


That one is not mine. I chose the pic because it demonstrated its use. Mine is effective but not as pretty.


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## bud16415 (Sep 5, 2021)

Eddie_T said:


> That one is not mine. I chose the pic because it demonstrated its use. Mine is effective but not as pretty.


I should make a wood one.

I made a hardened steel 5” sine bar when I was an apprentice way back. It calibrated within 20 millionths inch. Was good enough for the work I did.


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## Eddie_T (Sep 5, 2021)

I made mine 10" for convenience. I could have achieved greater accuracy by just making it and then calibrating it with a precise measurement but I opted for convenience of a x10 multiplier. I could still measure it precisely but it's OK for the pencil lines I work with.


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