I’m trying to generate the geometry for a specific triangle, and I’m stuck on how to do it. What’s especially frustrating is that it took me less that 5 seconds to do in Fusion 360, but in Grasshopper I’ve been stuck for hours trying to figure out how to set up the cluster to make it happen. I made this to try to explain it:

Points A, B, and Z are all on a line in that order. The length of AB is fixed at 12, and length BZ is an input that will vary from 0 to 1. I am trying to generate a point C such that angle ACB = 60 and segment CZ is perpendicular to AZ, for any given input of BZ within the range. Each value of BZ has only one configuration that satisfies this. (Note at s=0 triangle ABC will be a regular 30-60-90 triangle). Fusion handles this really easily, I can just place an undefined vertex C and once I have set angles ACB and AZC to these values, the geometry is fully defined and I can measure what X is out of this.

In Grasshopper though, I can’t find a way to set it up that doesn’t require X as an input parameter. I’ve tried various setups with the two trigonometry components, but my two defining angle measurements (ACB and AZC) don’t fit into one place that can determine the geometry. I have the lengths of AB and AZ for that trig, but not any of the other side lengths or angles. It’s not really that complicated and I know the math all checks out, I just can’t get Grasshopper incorporate the pieces. Can anyone think of a configuration that will do this? I really appreciate it, I’m totally stuck on this.