barely legal

*wins prize for most deceptive title ever*

I love it. I do it for fun. Yes, I'm talking about mathematics.
So, at work, doing math for fun today instead of doing my job, which is
totally not math related, I started thinking about...questionable...ways of
determining distances without actually measuring them. In particular, how
would the crews of my three lovely cannons ensure their ranges were correct?
Why, trigonometry of course!
The rules for firing the cannon say essentially "Don't meassure the distance
to the target." Well, what if I measure angles? Angles aren't distances.
Distances have units. Angles don't. Q.E. fucking D.

So lets say I put down two of my cannons a known distance apart. We'll call
this distance L. This is done in deployment, nothing sneaky about it.
Realistically, the second cannon isn't necessary, and just needs to be a
point a known distance from the other cannon. The bigger the value L, the
less effect a bad angle measurement will have on your results.
Then, in the shooting phase I decide I want to shoot something. I need to
get a good idea of range. So I measure two angles. One, angle A, is the
angle between the other war machine (Warmachine B) and the target, with the
focus of the angle being on Warmachine A.
The other angle, B, is from war machine A to the target at point B. Hard to
describe without a diagram, but its a non-binary group :)
so now I can do some calculations:
let t1 = L/( 1 + [ tan(A)/tan(B) ] )
let t2 = L - t1
Here comes the money shot:
the distance from A to the target is t1/cos(A)
the distance from B to the target is t2/cos(B)

tee-hee-hee! put your calculator in degrees friends, or measure those angles
in radians.
So even though I think this is somewhat legal, if very dodgy, I would
(probably) never do this. It was more a thought experiment. However, just
for fun I might go ahead and put some sort of protractor on the movement
trays of my cannons. Just in case.
I whipped up a spread-*** in excel to calculate it. Its all fancy, you
just plug in your three known values (L, angle A and angle B) and you get
your two distances.
There's multiple ways you can do this. For instance, if you can be sure all
your warmachines have the same y component of distance from the target (e.g.
they are all the same distance from your edge of the table) once you
determine one war machine's distance from the target, its a simple equation
to get ANY war machine's distance from the target without measuring any
further angles.
If you ask me about the derivation of those other methods, or this method,
I'll happily fill 20 pages in a veritible orgy of pedantic equations and
notes.
This will teach my job to assign me another dull task without supervision.

Oh yeah, my question: Is this even legal? I did a half-assed thumb through
of the rules and didn't see them saying you COULDN'T use trig.


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