# Resolving angle of parallelogram in 3D space

1. Nov 23, 2015

### Naton

Hi there,

I'm doing a bit of amateur scale model making as a hobby, building shapes out of flat-cut pieces. Trigonometry is a huge help with this, but I've hit a snag where I'm trying to calculate the angle of a particular parallelogram so it fits with the rest of the geometry.

1. The problem statement, all variables and given/known data

I've mocked up all of the variables from my situation into the following diagram with the angle I'm trying to determine marked as x:

https://zirung-sn3301.files.1drv.com/y3mjpry3qkCccqFTsqO8r5FMSn5iW1EOxg8zIyxIwBWd-K9eOxx_xsxBwu3Jqhu9f4S4W5EPP40fJnMqGBNe_ld4sSOf2zYCl0gRIAsvEUn3f_Za9Wg1nwQVSdFTg8TN3ifwWz6V0saeSPCEGmylsD_qxfzYBPptIN1dp5gQdHsuj8/math.jpg [Broken]

2. Relevant equations

3. The attempt at a solution
I have attempted to divide the shape into triangles so I can apply trigonometry to the problem, and even experimented with 3D trigonometry, however neither seemed applicable to finding a solution.
I know I haven't provided enough to deserve a full solution, but if anyone could point me in the direction of which mathematical principles I would need to study in order to solve this, I would be grateful and happy to read up on them and come back with my work (after all, I will need to do perform similar tasks in the future, so there's no point in just getting the answer to this one without learning to do it myself).

-Naton

Last edited by a moderator: May 7, 2017
2. Nov 23, 2015

### andrewkirk

I think the shape may be incompletely specified.
Call the parallelogram with the 65 and 115 degree angles P, and call the top right-angle triangle T.
Then the angle between the planes of T and P can change without disturbing any of the given measurements. We can visualize this with P being like a hanging sign that swings on hinges attached to the $\sqrt{3}$-length side of T.
I think that, as that angle changes, the angle x will change.