# Thread: What are the common triangles, OT, laying floors ??

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## What are the common triangles, OT, laying floors ??

I'm in the process of laying new floors in the house. What are the common size right triangles other than the 3-4-5?
When you do the a-square + b-square = hypotenuse math, you most always get a odd number with long decimal answers.
What are the common answer 45-45-90 triangles that can easily be measured on a fractional tape rule?
any other triangles easy to read on tape rule?

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For the 3-4-5 think in units. That is it can be inches, feet, yards ,6 inch=1 unit. You do not have to do the whole wall of a room, just most of the length that works out with your units.

So the sides can be 3-4-5 or 6-8-10 or 30-40-50 in what ever unit you choose. To put it another way (3x5=15) (4x5=20) (5x5=25) if your unit were 5.

for 45-45-90 triangle the two 45 legs are the same number/length and the long side is the length of a 45 leg time 1.414 (the square root of 2).

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Any multiples of the 3-4-5. 6-8-10, 9-12-15, etc.

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I first learned it in high school vocational ag class as 6-8-10. But any three numbers of that same ratio yields the same, though the larger numbers offer greater potential precision, . (i.e. measuring precision, not trigonometric precision.)

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For a 45-45-90 degree triangle...

multiply the short legs by 1.4142 to get the length of the long leg

Multiply the long leg by .707 to get the length of the short legs.

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As to the "odd number" issue, that hardly matters nowadays; everybody (except me) has a smartphone grafted to their body as an extra appendage, with a trig app always ready.

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Triplets such as 3,4,5 are termed Pythagorean triples. You can learn more about the subject at this Wikipedia article...

https://en.wikipedia.org/wiki/Pythagorean_triple

Copied from that article, here are some of the possible Pythagorean triples...

(3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25)
(20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53)
(11, 60, 61) (16, 63, 65) (33, 56, 65) (48, 55, 73)
(13, 84, 85) (36, 77, 85) (39, 80, 89) (65, 72, 97)

(20, 99, 101) (60, 91, 109) (15, 112, 113) (44, 117, 125)
(88, 105, 137) (17, 144, 145) (24, 143, 145) (51, 140, 149)
(85, 132, 157) (119, 120, 169) (52, 165, 173) (19, 180, 181)
(57, 176, 185) (104, 153, 185) (95, 168, 193) (28, 195, 197)
(84, 187, 205) (133, 156, 205) (21, 220, 221) (140, 171, 221)
(60, 221, 229) (105, 208, 233) (120, 209, 241) (32, 255, 257)
(23, 264, 265) (96, 247, 265) (69, 260, 269) (115, 252, 277)
(160, 231, 281) (161, 240, 289) (68, 285, 293)

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Ah yes, the pythagorean triple is what Im looking for.
All those are easy numbers to see on a common tape rule. But, those whole numbers end up with triangles tall and skinny.
Is there a way to see the triples in 1/2" increments? maybe that will yield triangle sizes useful in house rooms.

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Originally Posted by Ringo
I'm in the process of laying new floors in the house. What are the common size right triangles other than the 3-4-5?
When you do the a-square + b-square = hypotenuse math, you most always get a odd number with long decimal answers.
What are the common answer 45-45-90 triangles that can easily be measured on a fractional tape rule?
any other triangles easy to read on tape rule?
That's where a metric tape measure shines. If you have one marked with both imperial and metric it's also a converter from one to the other.

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