The thing that throws most people about the wind triangle is that if you take a direct crosswind from the left of say, 10 knots...
And you make it a 45 degree off runway-heading crosswind of the same strength...
You end up with 7.1 knots on the nose, and 7.1 knots on the left side.
People unfamiliar with wind vectors then try to do this mental math, which isn't right... 7.1 + 7.1 = 14.2 ... and end up all confused... "Hey, how'd the wind force get stronger?! It's only 10 knots of wind!"
That's what makes it totally non-intuitive for most folks.
"Half" the angle, "half" the crosswind component? No.
Swing it around to where it's 30 degrees off the nose, now it's 8.7 knots on the nose, and 5.0 knots on the left... which is where "intuitively" you'd think it would be at 45 degrees.
The 30 degree rule always works... "If the wind is within 30 degrees of the nose, the crosswind component will always be half or less, of the total wind speed."
That rule can actually be applied QUICKLY without pulling out a whiz wheel.
Know how many instructors have ever mentioned that one to me? One.
Know how useful it is when you hear a wind report on ASOS or ATIS that's within 30 degrees of the runway heading? Very. Chop the wind speed in half and you know your crosswind component is that or below.
Anything beyond 30 degrees off runway heading, just assume the whole damn thing is crosswind unless you're talking huge winds you shouldn't be flying in, anyway. At lower numbers, it's close enough.