Laying out a large 90 degree angle

StanFoster

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I am laying out a 90 degree stairway this morning in my stairshop. The first thing is I need a dead on accurate 90 degree angle layed out for the beginning and ending of my curved stairway.

I have seen many different ways of doing these....some use a 3-4-5 foot triangle.....some let a laser do it for them, some just take a framing square and use long straight edges.

The laser method is ok if you can verify its sends out laser beams that are 90 degrees apart.

The 3-4-5 foot triangle is ok, but you have to be very accurate projecting the lines out from the right angle of the triangle.

I simply use my calculator to draw it as accurately as I can.

This is simple trig for many here...but there are some that could learn such a simple yet most accurate way to lay out a large 90 degree angle.

The stairway I am laying out has a 124.5 inch radius outside stringer that must be marked off exactly at 90 degrees.

The first picture shows some poster board stapled to the plywood in an arc. I drew the 124.5 inch radius arc on that poster board...and picked a point near one end where I wanted one side of the 90 degree angle to be.

I am simply figuring a right triangle whose 90 degree sides are 124.5 inches long. If you square 124.5 you end up with 15500.25. Double that and you arrive at 31000.5. Take the square root of 31000.5 and you come up with 176.069 inches. That is the one and only length that when both ends of the 124.5 inch legs are apart....will the legs be right at 90.000 degrees.

The 2nd picture shows a small drawing of what I have drawn out full scale for the stairway.

I place a small nail on one end of the 124.5 inch arc....and make sure its adjusted to allow for the hook on the tape. I simply draw an arc of 176.069 inches....rounded off to just 176 and 1/16 inch....and where this arc intersects the 124.5 inch arc.....its exactly 90 degrees.

The last picture is a stretched line that falls right over the intersection. That string is dead on 90 degrees from the other side of the triange.

Quick and very accurate.

Stan
 

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All that math make my head hurt! Very cool Stan!
Stay safe.
 
Ahh yes... the old pythagorum theorum..


The sum of the squares of two sides of a right triangle are equal to the square of the hypotenus...
 
Yepper

Yepper

Ahh yes... the old pythagorum theorum..


The sum of the squares of two sides of a right triangle are equal to the square of the hypotenus...

A (sqaured) x B (squared) = C (squared)...Yes???

Stay safe.
 
A squared + (plus) B squared = C squared

your example:

3 squared = 9 A
4 squared = 16 B
5 squared = 25 C
9 + 16 = 25 C
 
Absolutely correct...I just hit the wrong key when I typed it! Thanks for the correction.
 
That is the same theory as you use to lay out on a floor or any flat surface using the 3-4-5. You just used 1-1-1.414. The 1.414 is rounded off but works for most things. Cool how those tricks work.
 
If you want to save the math and if you have room, lay out all four sides of the square and make sure you see the exact same distance measured corner to corner both ways.
and if you wanna get real fancy dont forget the coefficient of expansion for steel (depending how hot it is)
 
Stan if I needed a 90 degree line I have done it many times by making a mark somewhere along a straight wall and measuring out along the wall an equal amount on both sides of the mark, as far as possible. Strike an ark from each point out into the room as far as possible and where the two arks cross will be 90 degrees straight to that center mark.
 
And if you want a LARGE square an optical prism will give a square as far as you can literally see.Love mine, people look at me like a witch when I use it
 
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