Personally, I have always wondered about the prominent position trigonometry and geometry get.
As it is typically taught, it is the most useless thing, the time spent there would be much better spent on algebra, calculus.
From basic theorem of algebra flows trigonometry and a lot of number theory, while from calculus with some linear algebra flows geometry.
For a lot of people, geometry is their primary or perhaps only exposure to proofs. Not that everyone needs to understand proofs in their day-to-day lives, but it's a good mental discipline to at least be exposed to, and geometry proofs are fairly straightforward and relate to things that many people will have a good intuition to convince them that the thing proved by each correctly-constructed proof is really true.
Also, geometry gives students something concrete to visualize, and so might be easier for some to understand than more abstract kinds of math.
Maybe trig is over-emphasized at the high school level, but it is pretty useful in a lot of real-world situations, and it's easy to apply without having to know a lot of other stuff.
From what I can tell, proofs are gone. I got my daughter all excited about geometry, by promising her that she could do proofs. The curriculum was almost exclusively focused on problem solving based on remembering formulas. She went ahead and did all of the proofs anyway.
IMHO, high school math misses the one course that would be most useful to the students. Statistics. While there are a LOT of statistical models that aren't especially useful in every day life, knowing the most common ones can be a big help.
Of all the math classes I took in college the only one I use on a regular basis is statistics. Thinking back on high school I spent a whole lot of time on basically calculus prep and in the end I hardly ever take a derivative or integral of anything.
I always found trig and geometry to be the most interesting and useful part of math. It maps pretty well onto real things that you might have to do. Maybe this is more relevant in the rural area I grew up in, but geometry and trig is really useful when you're trying to do carpentry, or figure out if you've got room enough to chop down a tree, pathfinding on a map, etc.
Trig is a pretty useful subject for the skilled trades. Framing a house, as mmmpop notes, but also things like plumbing and cement work. If you don't go on to college, or you don't major in engineering or math, calculus is pretty useless. I've never once used calculus outside work, but I have used trig.
So I guess you've never framed up a house have you? Basic trig is so incredibly important to anyone that ever desires to build a thing. Don't you remember learning the unit circle in Calc 2??
trig has seemed extremely important to me. specifically using sin and cos. helps a lot in physics as well as computer graphics and many other applications.
As it is typically taught, it is the most useless thing, the time spent there would be much better spent on algebra, calculus. From basic theorem of algebra flows trigonometry and a lot of number theory, while from calculus with some linear algebra flows geometry.
The rationale is probably history.