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This is a little problem that I encountered while trying to measure the floor plan of an irregularly shaped reverberation chamber. I have measured the length of the four walls (all of different lengths). However I didn't measure the angles at the corners (which are in general not 90°), thinking that it would be trivial to find this later.

The first question is: Is it possible to determine the angles from this amount of information? I would say yes as we have 4 knowns (the lengths), and 1 unknown angle (once we have one angle can use cosine rule to get the diagonal and the problem is simple)

If someone can clarify it is possible to find the angles from this much information, that would be fantastic.

Second question: where to go from here? I really want to get this by myself, so no answers (yet). I've playing around with the cosine/sine rules, but with no success. Its not quite as simple as it looks (unless I'm missing something obvious).

Third question: Why don't I just go back and measure the angles? Good point, but its bugging me now...

It'd also be interesting to look at the general case (any number of walls) but I'll try the 4 walls case first!

The first question is: Is it possible to determine the angles from this amount of information? I would say yes as we have 4 knowns (the lengths), and 1 unknown angle (once we have one angle can use cosine rule to get the diagonal and the problem is simple)

If someone can clarify it is possible to find the angles from this much information, that would be fantastic.

Second question: where to go from here? I really want to get this by myself, so no answers (yet). I've playing around with the cosine/sine rules, but with no success. Its not quite as simple as it looks (unless I'm missing something obvious).

Third question: Why don't I just go back and measure the angles? Good point, but its bugging me now...

It'd also be interesting to look at the general case (any number of walls) but I'll try the 4 walls case first!

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