Why would 3/4/5 right triangles be useful for carpenters? 30-60-90 are definitely useful though.

In layout, to determine a right angle longer than your framing square. We measure multiples of 3/4/5 on perpendicular walls to check their square, and then measure diagonally corner to corner to check again.

Not parent, but I was also confused by the tool -- if the square (which is by definition 90 degrees where the two sides joined) is x and y long on the two sides -- then what's the purpose of being able to make a square from the 3/4/5 rule that's limited to the x and y lengths?

I'm having trouble explaining more succinctly why this seems like a totally pointless feature of a woodworking square - so it's possible I've misunderstood how it could be used to extend beyond the length of its arms.

I just meant for a larger project we lay aside the square, and measure out 3/4/5 on the ground or whatever. So you're gonna dig the foundations of a house, use a string line and measure out 30 feet and 40 feet. If they're 50 feet apart, you're good.

Oh I understand your question now, yes I agree.

To make sure your 90 is really a 90. Easy and quick to check.

You can do that with the square itself.

You can check the corner is square with a square. Checking the walls and the room can be done with a string.

a^2 (9) + b^2 (16) = c^2 (25)