Armada's rules for establishing firing arcs, firing ranges, and lines of sight are somewhat complicated. I've thrown a few diagrams together that (I hope) explain them better than the rulebook does.
The full album is here: http://imgur.com/a/fs1ni
(EDIT 4/20/2015: Combined images into one. Clarified range/LoS not arc-bound.)
(EDIT 5/8/2015: Range measurements restricted to arc as per new errata.)
(EDIT 12/20/2016: Blocked range check lines also block LoS and attacks, per an old FAQ that I missed.)
(EDIT 2/5/2018: address blocked range checks more directly)
Edited by Quarrelupdate