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best way to verify a 45 degree angle?

26K views 45 replies 16 participants last post by  PrestigeR&D 
#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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#2 ·
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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#3 ·
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?
 
#4 ·
#8 ·
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.
 
#11 · (Edited)
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*
 
#17 ·
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:
 
#16 ·
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
 
#23 · (Edited)
I'm willing to bet it will be over an inch out. At least. Sometimes these guys are an inch out over 10':blink: I had to use a triple rim board on an entry way once.
 
#24 ·
Didn't read all the other posts so sorry if its already been said.
Knowing the lengths of the 3 sides you can use the law of cosines.
c^2=a^2+b^2-2abcos(C)
The C angle is across from the c side, using this for all sides you can determine all angles. Or you can find the one angle and then use the easier law of sines.
 
#29 · (Edited)
Verify that the back wall and side wall are square to each other first.

Measure length of side wall to corner. Measure length from back wall to long point of angle wall. Subtract to find the difference. Use this number as the lengths of a right triangle and calculate the diagonal. If your angle wall is a 45, the number won't lie.

Example: Side wall is 30 feet. Length from back wall to point is 40 feet.

This leaves 10', or 120". Diagonal of 10' is 169.705".

If your diagonal doesn't match this length, the angle is off.

The same can be accomplished with unsquare reference walls by snapping square lines on top of the walls.

As for the 45 wall, you only need two numbers to establish a 45. Never trust the mason.
 
#36 ·
The reason I didn't us the "blue lines" to help is, I don't know if one or both or none of those walls are correct either. (not yet) So using that a benchmark to verify anything would likely not work out.
 
#33 ·
JT,

I mentioned in an earlier post to use a calculator to find the sine. If you have an iPhone with iOS 7, you can use the calculator in Control Center (swipe up from bottom to access), turn the phone to landscape you have a scientific calculator with the trig keys. My guess is Android has something similar.

Tom
 
#38 ·
This is realistically the way I am going to verify this and other 45 degree corners from now on.

It's simple and easy for me personally to understand.
 

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#40 ·
Whatever way is the easiest for you to undrestand is the best way.

I'm just suggesting to you that using the width of your rectangle is all you need to create the two black lines of your triangle, or the blue lines I made.

Since your black lines are 24', the width of the yellow lines in the rectangle should be 33' 11-5/16".
 
#44 ·
JT,

For marking the foundation and getting the exact measurements down and the correct 45° angle...all you need to do once you have the rectangle marks and lines square is pull off the corners of right side of the drawing wall 24' until the two 24' lines bisect each other. That sets your 45° mark and you snap your 24' lines from there.
 
#45 ·
I just wanted to re-iterate, this did NOT have me stumped. :laughing:


This is a plan view of the house. (I had some plans at home that I quoted from)

We only had about 45 minutes on Friday to work on the layout. So we spent maybe 3 minutes scratching our heads.


The picture probably show a bit more clearly. Baring measuring off of a suspended string line,in the middle of nowhere. I do not see a way that I could have gotten the 45 on site without using the math we were discussing. Like I said, the walls are not friendly to making square corners.

I would have gotten it anyway, but I was interested in the way to mathematically get the answer. If for no reason, than to verify my work.

working through this thread helped me remember things I used to know, and learn a few new ways too. :thumbsup:
 

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