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I don't think I understand the full question about the triangle. I can't tell which plane it's sketched on. Can you describe your end goal a bit more?
But the x-axis of the planes can be a bit unpredictable. As I understand it this is actually a math limitation more than a code limitation as demonstrated by the hairy ball theorem. If you look at the images in that link and imagine the "hairs" as the x-axes of all of the possible planes you may see what I mean.
Not sure what you are trying to do but one thing to consider would be to use a mate connector instead of a plane, that way you have explicit control of the axes.
sine of angle = opposite side / hypotenuse
cosine of angle = adjacent side / hypotenuse
also unclear what you're trying to accomplish.
Others can correct me if I'm wrong, but each part studio only has one origin - and it is the intersection of the front, right, and top planes (planes that you create, do not have origins). You can use the "use" command to reference the origin onto a new sketch that you have created but this reference point will always be "normal" to the plane you are sketching on. If I understand what you want about the triangles, you could just edit the sketch with the triangle and dimension all the sides,and angles you need (and don't forget about constraints).
If you are new to OnShape, I would take the self paced learning courses in the learning center, there is a lot of good information in there (most courses are free - but some aren't). Keep at it.
@jg_k
In the below document, I use a MultiMate Connector as a Plane
WHEN I CREATE A NEW PLANE IN ONSHAPE, IS THERE ANY PATTERN IN THE X-AXIS OF THIS PLANE?Try using a HORIZONTAL CONSTRAINT to get something along the X axis
I want to find the correspondence between the old origin and origin of the newly created plane
The document below is a way of using right triangleS to see how the unalterable origin in the program relates to a point within another plane
https://cad.onshape.com/documents/914965badce1554516e9120c/w/fa75b31f9de48e9ff76a6b58/e/61839948da753373aecd1b9c
Can someone tell me how to calculate the two adjacent sides of a right angled triangle in the diagram?
The document also gives all the dimensions of the right triangles which in this case, eliminates any calculating. In one case the USE TOOL is used to bring the lines into a sketch and then dimension.
IN THE DOCUMENT ABOVE, STEP THROUGH THE LIST ON THE LEFT TO SEE HOW THINGS WERE CONSTRUCTED