Q:

Calculating the distance when shooting at a flying foe

Lets say that a foe is 30' away and 20' up in the air. 
Using trigonometry, that gives a distance of 30^2 + 20^2 = 1300 sqrt(1300) = 36.06 ...but I don't believe Pathfinder expects folks to use trig to figure out range increments.
Is there a rule that covers this? I can't find it but my impression was that one actually just takes the larger of the two values (so if someone is 100' away and on one dimension and 50' away on another, it's still just a range of 100').

A:

I can't find the exact rule on the Pathfinder SRD, but there's a link to a topic here that describes it:
http://paizo.com/threads/rzs2n3i9?Question-about-diagonal-movement
And this is the rule in the D20SRD, which I'm pretty confident is the same:
http://www.d20srd.org/srd/combat/movementPositionAndDistance.htm
You might find the exact rule in your rulebook somewhere (but I don't have one to check, unfortunately)
It essentially comes down to this:
Diagonal movement
Every other square of diagonal movement is counted double. So the first square is 5ft, the second is 10ft, the third is 5ft, etc. This approaches the actual diagonal reasonably over short distances.
So in your example, the distance would be 10ft going straight (30ft-20ft) and then 20ft going in a pure diagonal (the lowest of the two) with every other square counting double; ie the distance multiplied by 1.5x, which gives 30ft of diagonal movement for a total of 40ft travelled.
The rule you remember of "take the highest" is from 4th Edition D&D.
(As you can see the final result comes within 5ft of the trig answer, so it's accurate enough for game purposes)

