Is there only ONE "right" triangle?

I've been a fan of Triangle Man for some time... Then the other day... years, and decides later I saw this Hugh Lieber art work.

Hugh Lieber

And once again I fell for Triangle Man.  And that got me thinking of the 3-4-5 right triangle... When I think of right triangles - it's the one I imagine...  although I spent many years using the classic drafting 30-60 degree triangle.

And then this sound track starts in the back of my mind...

THEY MIGHT BE GIANTS

Particle Man (Tiny Tunes)

Lyrics

Particle man, particle man
Doing the things a particle can
What's he like? It's not important
Particle man

Is he a dot, or is he a speck?
When he's underwater does he get wet?
Or does the water get him instead?
Nobody knows, Particle man

Triangle man, Triangle man
Triangle man hates particle man
They have a fight, Triangle wins
Triangle man

Universe man, Universe man
Size of the entire universe man
Usually kind to smaller man
Universe man

He's got a watch with a minute hand,
Millennium hand and an eon hand
When they meet it's a happy land
Powerful man, universe man

Person man, person man
Hit on the head with a frying pan
Lives his life in a garbage can
Person man

Is he depressed or is he a mess?
Does he feel totally worthless?
Who came up with person man?
Degraded man, person man

Triangle man, triangle man
Triangle man hates person man
They have a fight, triangle wins
Triangle man

Songwriters: John Flansburgh / John Linnell / John C. Flansburgh / John S. Linnell

Particle Man lyrics © Warner/Chappell Music, Inc