"can" lights -- advice

plan to install "cans" in the kitchen
I have a box (18) of par20 bulbs, so would like to use those
par20 seems more sized for a 5" can, but I'm not that opposed to a little imperfection of using a 6" can
my ceiling is 8' and countertops are standard, 3'
how far apart should the cans be to give good light? so 5' of travel and a 30 degree beam.
a little math suggests the 2 * tan15 * 5' = 2.67' (32")
is that accurate? other considerations
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That's the dimension of the beams. However, placing them like touching circles of light may not be the best way to illuminate.
Consider (with circles larger)
O O O O O
and
O O O O O O
As well as various other patterns. It's probably easiest to arrange the lights on a table the same distance away from the wall as they will be from the countertops, and have a play.
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