It's a trigonometric model
Is it. Do you think that a snooker player unconsciously works out sines and cosines? I'm sceptical on that point.
No, I don't, because sin and cosine are arithmetic tools to assist in making trigonometric assessments more accurate.
I tend to think maths is a bit more than looking at two balls and estimating what a right angle looks like.
Maths is quite a lot more than that - in exactly the same way that English is more than just looking at the sentence 'See spot run' and noting the lack of capitalisation for the proper noun... but that's part of English, and the assessment of angles in relation to one-another is part of maths, specifically part of trigonometry.
At its simplest it's a visual assessment and an estimate 'This is bigger','this is smaller', 'these are the same'... Then you develop more refined - arithmetic - tools to calculate to greater degrees of precision, or you apply logical principles to determine that certain situations MUST be a certain way without the need to resort to arithmetic.
It's the most basic form of trigonometry, perhaps, but if more people were aware of ideas like that then perhaps fewer people would be afraid of maths and we wouldn't be in a situation where parents see it as some wierd badge of honour to tell each other how their ten year old's maths homework is beyond them.
O.