Why is the tangent of 22.5 degrees not 1/2? Sorry for the stupid question, but why is the tangent of 22.5 degrees not 1/2? 
(Okay... I get
 that that the tangent of 45 degrees is 1 ("opposite" =1, "adjacent" =1, 1/1 = 1.  Cool.  I am good with that.) Along those same lines, if the "opposite" drops to 1/2 relative to the "adjacent" i.e., "opposite" = 1, "adjacent" = 2 therefore 1/2. What am I missing?  Thanks in advance for your help.

The basic error being made is the assumption that you are converting one unit into another unit such as when you convert meters into yards.  Degrees are units but tangent represents a ratio.
