Help with geometry

[doug_w]

I'm trying to layout the six sided shape shown to roughly the same proportions. I know I want the top to be .5" per side and the height (of the side, not the complete shape) to be 6". The bottom dimension would be somewhere around 2" but what is the formula for figuring out the exact dimension? I would work it out by trial and error except I have several of various sizes to layout.
Thanks for any help,
Doug

[ccogg]

The bottom can be anything you want (less than 12.5 in). It’ll just change the angle of the sides and the overall height of the finished piece.


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[el perro]

Pythagorean theorem; x squared + y squared = h squared.

Works for right triangles.

SOHCAHTOA. sine = opposite/hypotenuse

Cosine = adjacent/hypotenuse

Tangent= opposite/adjacent.

[doug_w]

Thanks! That's kind of what I thought but when I tried one with a 2.75" base by the time I got around they were not matching up, probably due to poor layout. I'll give it another try.

[doug_w]

Thanks el perro. A bit beyond my skills but I do want to learn more math so I'll research more. How do you apply these formulas to non-triangles?

[MetalMan23]

This is quite simple, just draw a hexagon that is the size that you want the base to be, and that will give you the measurements

Also when dealing with trapezoidal shapes just cut them into triangles that makes the math easier.


What do you mean they didn't match up? What material are you working with?

[MinnesotaDave]

For non-triangles it works by drawing triangles where you need them.

Then the straight sections between are rectangles.

[doug_w]

This is quite simple, just draw a hexagon that is the size that you want the base to be, and that will give you the measurements

Also when dealing with trapezoidal shapes just cut them into triangles that makes the math easier.


What do you mean they didn't match up? What material are you working with?

I cut out a test piece in cardboard and taped them together. When I taped the first to the last it didn't sit flat but like I said they probably weren't very accurate. The final will be 12 or 14 gauge steel.

[Virgil5]

There are online calculators.
http://www.1728.org/quadtrap.htm

[docwelder]

I cut out a test piece in cardboard and taped them together. When I taped the first to the last it didn't sit flat but like I said they probably weren't very accurate. The final will be 12 or 14 gauge steel.

my math skills are rudimentary at best. i had to make a dozen flagpoles from streetlight poles and used the cardboard method for making that 6 sided shape for pigeon proofing pole tops. both the layout and bird proofing worked well.

[jakedaawg]

I cant wait for opus to enlighten us on this...

[MetalMan23]

I cut out a test piece in cardboard and taped them together. When I taped the first to the last it didn't sit flat but like I said they probably weren't very accurate. The final will be 12 or 14 gauge steel.

If they didn't sit straight then you didn't cut all the piece the same, IMO there's no real reason to make a template you can figure it out with math without wasting time

[MetalMan23]

I would cut the pieces out of a sheet like this, https://images.platforum.cloud/uploads/201...0da972241a.jpg

[Country Metals]

The easiest and stupidest (no pun intended) is to take a 2' square and drawn a 90* angle on the table in soapstone. Then draw a vertical line 1/4" away. This gives you 1/2 of your top width. Then take a compass and set it to 6" and put it in the end of the 1/4" mark. Now draw a arc. Anywhere on that arc is where it can be. Now pull off the original square line and you can get all your measurements.

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[doug_w]

Thanks for everyone's help. Was pretty easy once I got my layout more exact. Ended up laying them out like you suggested metalman. Tacked in pairs then tacked the pairs together. Took a little nudging to get the last ones line up.

[el perro]

Looks good from here!

[docwelder]

very good job.

[MinnesotaDave]

Excellent

[Kelvin]

Handy trig calculator for future reference/bookmarking:

http://www.carbidedepot.com/formulas-trigright.asp

I use it all the time...

[n00b]

I think the thing is that this trig **** is a little intentionally overcomplicated so that regular folks can't learn it. I'll do my best to explain. I tutor kids in math to get money for welding supplies.

You can think of this sin cos tan **** as just random names like bill joe and ty. The important thing to know is that they are ratios like 3 apples to 2 oranges as a 3" side to 2" side in a triangle. You remember the ratios by some indian chief who was actually a relative of geronimo. He is called soh cah toa. Sin (angle) = opp/hyp (soh). Cos (angle) = Adj/hyp (cah). Tan (angle) =Opp/Adj (toa). Basically you feed it an angle for lunch and it will crap out the ratio of the sides as a decimal. If you take tan(45 degrees), it will crap out 1. Which means the opposite and the adjacent side are each 1 unit. You can think of hyp or hypotenuse is the fattest mutant side of a triangle. Adj. is the side that's hugging the angle while also not the fattest side. And Opposite is the side that is directly opposite.

So lets say we have a have a road that starts at sea level and goes on with a 26 degree grade that goes for 10 miles via the mile markers. We want to know A: how many miles up in elevation are we. We know the angle, 26 degrees. We know the hypotenuse, 10 miles. But we don't know the X axis length, or the adjacent. And we don't know the Y axis length, the opposite. So we smartly pick the sin ratio. not cos or tan as it won't work. sin(26 degrees) = opp/hyp which is sin(26) = elevation/10miles. We type in sin(26) into our calc and we get 0.43. Make sure that you calc is in degree mode. That means the opp side is 0.43 units and the hyp is 1 unit. The problem is we arent done. We don't know what 1 unit equals. It could mean years till i die or how bad your wife drives. But since we know its 10 miles we are all safe and alive. Since these are all ratios. we say 0.43unit/1unit = elevation/10miles. By solving for elvation we get 4.3. So our elevation is 4.3 miles.

To calculate the angle based off the elevation and road mile markers you cant use sine. You need to use arcsin. The sin function eats an angle and poops out a ratio. The arcsin function eats an angle and craps out a ratio. Another name for arcsin is sin^-1. The calculator labels it sin^-1 to cut printing costs and to save letters. The arc sin function is the exact opposite of the sin function. They are the ying and the yang. So you run arcsin(ratio)=angle so arcsin(4.3 opposite/10 hyp) and we get arcsin(0.43) which equals 25.46 degrees. The reason its not exactly 26 degrees is because i rounded the 4.3 instead of 4.3blahblachblach. To get more precision use more decimal places. Hope this helps. BTW I am not bad at math and blah at welding. If you are in NJ NY PA area, I can teach you all the layout trig geo math as well as a few tricks and short cuts like if a wire spool's cable is rolled out how much feet is it or if a spring is uncoiled how long it really is in simple terms in exchange for welding lessons. Doc Welder? I NEED WELDING HELP LOL, I LITERALLY CANT TEACH MY SELF. CANT KEEP A STEADY HAND. Cheers

[MetalMan23]

Thanks for everyone's help. Was pretty easy once I got my layout more exact. Ended up laying them out like you suggested metalman. Tacked in pairs then tacked the pairs together. Took a little nudging to get the last ones line up.

Looks great, good job

[MinnesotaDave]

I think the thing is that this trig **** is a little intentionally overcomplicated so that regular folks can't learn it. I'll do my best to explain. I tutor kids in math to get money for welding supplies.

What a load of crap.

I teach math and kids tell me all the time "That's all it means? Well that's easy."

It only sounds hard.

And your long rambling statements tuned my brain out nearly immediately.

Get to the point already. Brevity is your friend.

The formulas are tremendously short and simple - your statements can be too.

[MetalMan23]

Math is easy once you can get someone to explain it to you in simple terms,

[MinnesotaDave]

Math is easy once you can get someone to explain it to you in simple terms,

Agreed

[docwelder]

I think the thing is that this trig **** is a little intentionally overcomplicated so that regular folks can't learn it. I'll do my best to explain. I tutor kids in math to get money for welding supplies.

You can think of this sin cos tan **** as just random names like bill joe and ty. The important thing to know is that they are ratios like 3 apples to 2 oranges as a 3" side to 2" side in a triangle. You remember the ratios by some indian chief who was actually a relative of geronimo. He is called soh cah toa. Sin (angle) = opp/hyp (soh). Cos (angle) = Adj/hyp (cah). Tan (angle) =Opp/Adj (toa). Basically you feed it an angle for lunch and it will crap out the ratio of the sides as a decimal. If you take tan(45 degrees), it will crap out 1. Which means the opposite and the adjacent side are each 1 unit. You can think of hyp or hypotenuse is the fattest mutant side of a triangle. Adj. is the side that's hugging the angle while also not the fattest side. And Opposite is the side that is directly opposite.

So lets say we have a have a road that starts at sea level and goes on with a 26 degree grade that goes for 10 miles via the mile markers. We want to know A: how many miles up in elevation are we. We know the angle, 26 degrees. We know the hypotenuse, 10 miles. But we don't know the X axis length, or the adjacent. And we don't know the Y axis length, the opposite. So we smartly pick the sin ratio. not cos or tan as it won't work. sin(26 degrees) = opp/hyp which is sin(26) = elevation/10miles. We type in sin(26) into our calc and we get 0.43. Make sure that you calc is in degree mode. That means the opp side is 0.43 units and the hyp is 1 unit. The problem is we arent done. We don't know what 1 unit equals. It could mean years till i die or how bad your wife drives. But since we know its 10 miles we are all safe and alive. Since these are all ratios. we say 0.43unit/1unit = elevation/10miles. By solving for elvation we get 4.3. So our elevation is 4.3 miles.

To calculate the angle based off the elevation and road mile markers you cant use sine. You need to use arcsin. The sin function eats an angle and poops out a ratio. The arcsin function eats an angle and craps out a ratio. Another name for arcsin is sin^-1. The calculator labels it sin^-1 to cut printing costs and to save letters. The arc sin function is the exact opposite of the sin function. They are the ying and the yang. So you run arcsin(ratio)=angle so arcsin(4.3 opposite/10 hyp) and we get arcsin(0.43) which equals 25.46 degrees. The reason its not exactly 26 degrees is because i rounded the 4.3 instead of 4.3blahblachblach. To get more precision use more decimal places. Hope this helps. BTW I am not bad at math and blah at welding. If you are in NJ NY PA area, I can teach you all the layout trig geo math as well as a few tricks and short cuts like if a wire spool's cable is rolled out how much feet is it or if a spring is uncoiled how long it really is in simple terms in exchange for welding lessons. Doc Welder? I NEED WELDING HELP LOL, I LITERALLY CANT TEACH MY SELF. CANT KEEP A STEADY HAND. Cheers

noob; i didn't have the patience to wade through your long post until now. thanks for the math help offer but i got through almost 50 years of weld/fabrication with my shaky math skills so i figure i can struggle through the next fifty. if we can work out logistics i'll be more than glad to help you out. shoot me a pm and we'll go from there.