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Discussion Starter · #1 · (Edited)
Refresh my memory,

We are just starting a new frame, and I can't seem to remember how to mathematically verify the 45 degree angle on this foundation wall.

Normally the other (parallel) walls are long enough on a house, that I can run a 90 degree angle and get it that way.

So this is what I have.


The yellow lines are established as square.
The red circle is a 45 degree.
What I want to know, is

can I deduce the length of the red line given the length of the black lines, and the angle of the red circle?

For instance, If I pull the tape 24' on each black line, I get 44' 4"1/8 as the red line measurement.

BUT I cheated, I used sketchup.:laughing: Before Sketchup as invented, I would have run string lines and tried to get parallel measurements fron the string.

Anybody know the proper formula for this?

Thanks:thumbsup:


BTW what A nice view on this Acreage!
 

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Are the lengths of the black lines the same? A line that bisects the point in the circle will create two equal right triangles. From there, Pythagoras takes over.
 
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Discussion Starter · #3 ·
Are the lengths of the black lines the same? A line that bisects the point in the circle will create two equal right triangles. From there, Pythagoras takes over.

I can make the black lines what ever I want them to be.


I know what you mean, But I need to VERIFY the 45 degree corner is actually 45 degrees. Which means I need to be able to find out what the length of the red line based on what the angle is and my given (black lines) does that make sense?
 

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Discussion Starter · #6 ·
If i am not mistaken you could use sine or cosine law to figure it out. Or if possible, create a 90* and bisect it.
I am quite curious to find out the solution to this!
Normally I would do the 90 and bisect, but there isn't any walls long enough to do it.:rolleyes:
 

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Half of your 44' 2 1/8" line is 22' 2 1/16". 2- 22 1/2 deg right triangles form a 45. So diagonal is 13" per foot. (13"/ft) X 22' 2 1/16 = 24' 1/4". You're off like a 16th in 22 feet.
 

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It's an isosceles triangle so;

Base angle sin (180° - 45° = 135°/2 = 67.5°) =0.92388

0.92388 x 24’ = 22' 2 1/16” (base of the right triangle of 1/2 of the isosceles triangle) x 2 = 44' 4 1/8"

The rise is 9' 2 1/4".

Tom
Or what he said:blink:
 

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You could double check the 45° angle by marking the center of a pulled string across the base, then check the rise (9' 2 1/4" assumes your 2 legs are 24').

Tom
 

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Discussion Starter · #11 · (Edited)
You could double check the 45° angle by marking the center of a pulled string across the base, then check the rise (9' 2 1/4" assumes your 2 legs are 24').

Tom
Yeah, after I read your last post, I was planning to do that first thing in the morning. :thumbsup:


:laughing:

* edit, thanks guys I learned something valuable tonight*
 

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Yeah the isosceles triangle Whenever I see a triangle I always try and figure out a way to make a right triangle. Then 345 ;)

But it seems that they already beat to helping you.
 

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Design Build
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If you need to be 100% sure! set up batter boards around the foundation and extend the closer yellow line to the right with an actual string or laser.

Then you'll have a true reference line to pull from to check that upper right corner.
 

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When you normally bisect them how do you go about doing so? I guess on a wood subfloor its easy to strike arcs and locate intersection points.. but on a foundation with nothing there... How :eek:
Foundation layout relies on math. The excavator or the person placing the footings has nothing to measure from at first. Just to square up the the batter boards to dig the hole you need to us math. Once one corner is set you pull a length for the first wall, set the batter board with the over dig, using math you find the length of the diagonal to set the second corner square.

All the roofs you cut are nothing but isosceles triangles you turned into right triangles.

You gotta trust the math.

Tom
 

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Discussion Starter · #17 ·
If you need to be 100% sure! set up batter boards around the foundation and extend the closer yellow line to the right with an actual string or laser.

Then you'll have a true reference line to pull from to check that upper right corner.
I would have probably done that Friday, but the wind was at 30 miles an hour, so I wouldn't have trusted the string anyway:laughing:


I wasn't stumped with this anyway, I just wanted to remember the math for it.:thumbsup:
 
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