[conspire] Trig. - SAS and ASA, but no ... Re: Password permutations (was: Correction)

[Michael Paoli]

> From: Texx <texxgadget at gmail.com>
> Subject: Re: [conspire] Password permutations (was: Correction)
> Date: Thu, 16 Apr 2020 14:18:23 -0700

> If you have 2 sides and an angle or 2 angles and a side, and you know WHICH
> sides & angles you have, you can reconstruct the triangle

No, no, no.  Didn't you get taught in trig, there's SAS and ASA,
but you don't get ASS!

So, just think about it ...

SAS ... you have a fixed length side, you put in an angle,
put put your second side of fixed length.  Only one way left
to do a triangle - connect those two free ends, and you've got a
triangle - as long as your angle isn't 0 or 180 degrees, or any segments
of length 0, and you're good (unless you want to consider degenerate
triangles).

ASA - you lay down your fixed length segment.
You stick your angles on each end - each less than 180 degrees,
you orient your angles in the plane, so, extending them out, you'd have
lines that intersect.  There you go - one uniquely defined triangle
(at least to congruencies).  Again, ignoring degenerate cases.

ASS ... uh huh, put down an angle, attach a fixed length side,
now attach another fixed length side from that, with indeterminate
angle ... where can it in line drawn out other side of that first
angle?  Unless that last angle turns out to be exactly 90 degrees,
there are exactly two possible triangles (again, ignoring degenerates).

So, you get SAS and ASA, but no ASS.

Yes, order matters.