How to determine an arbitrary angle of rotation

WillAdams · February 21, 2024, 10:29pm

as requested on support…

The piece on the left is 90 degrees/square to the grid. The piece on the right has an angle that I don’t know. I want to rotate it however many degrees so those two edges meet perfectly.

which is pretty basic trigonometry.

We have done this sort of thing once before:

In this case, it’s pretty simple to draw a rectangle from the point of the rotation to the shorter angle (which length is the hypotenuse of the right angle which we need to measure).

Using the rectangle tool:

start at one end of the angled part:

control-drag-click at the node for the opposite end of the line:

to get the other two sides of a right triangle.

At:

we have some notes on this, including an image showing the formulae — and a couple of links to triangle calculators such as:

We plug in the numbers there. We want to solve for angle beta:

so we plug in the values for side a, 2.5736:

and side b, 1.67:

and we get:

so we rotate by −32.9794:

arriving at:

Done

which lines up as expected:

StuffSethMakes · February 22, 2024, 6:25pm

feature request: a “just do it for me” button, lol!!

Just kidding. Thanks for posting this. I’m going to try it and I look forward to putting it to use on other projects too!

-seth

StuffSethMakes · February 22, 2024, 6:37pm

I just tried this technique. Perfect! Thanks again for the education. I’m dumb and never would’ve known to find that angle this way. You guys rock!

WillAdams · February 22, 2024, 6:41pm

Like @KevBarn14 — you must have been out at a game on the day that was covered in Trigonometry class.

StuffSethMakes · February 22, 2024, 6:51pm

HA! Trigonometry class? What the heck is that? I was either playing baseball or making fun of math nerds.

Thanks again, I really appreciate it.

-seth

WillAdams · February 22, 2024, 7:00pm

Actually, I’m pretty sure that we went over this in Shop III as well.

See:

and

and to catch up on this sort of thing:

system · March 23, 2024, 7:00pm

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