[amluto]

I agree with your point in general, but I do find myself actually using trigonometry for fairly basic real-world purposes more often than one might expect. For example: how big of a piece of material fits in a particular position if it’s not parallel or perpendicular to the stuff around it? If a rope supports a load in the middle, how much tension does the rope need? How much of an angle should be cut into a door to comfortably clear the jamb? (If you’ve never contemplated this before: a door with a rectangular cross-section will have less clearance to the jamb when almost closed than when fully closed.)

[Terr_]

> If a rope supports a load

Rambling off-topic, but I remember being very impressed at how a uniform hanging rope makes a catenary [0] shape which is related to making strong structural arches.

So maybe if the students were somewhere where the class could design and make an igloo... :p

[0] https://en.wikipedia.org/wiki/Catenary

[amluto]

Fun exercise for the reader: if you have that uniform hanging rope support a uniform flat suspension bridge (via a bunch of closely spaced vertical ropes), and the bridge is much, much heavier than the ropes, then you get a parabola instead of a catenary. Wikipedia gives a derivation involving differential equations, but it glosses over the actual fundamental difference between these situations. But you can explain what’s going on with just trigonometry and no calculus, let alone differential equations: consider how much weight a small section of chain that isn’t right in the middle is supporting. You’ll end up with a drawing involving a right triangle and some numbers associated with the sides, and those numbers will line up differently with the opposite, adjacent and hypotenuses in the two cases.

So your off-topic rambling isn’t off-topic at all :)

[lovehashbrowns]

I think for me personally although I don’t use maths often enough in any practical sense, the one thing I think has stopped me progressing in life how I feel I want to has been my lack of maths knowledge. I don’t mean in a career sense but in an enjoyment sense. I watched a video about proving that the square root of two is irrational and that made me irrationally happy, and I’d love to keep going but a lot of the maths in other proofs or concepts gets absolutely insane. I don’t know how to express that to kids learning maths for the first time, though. It also almost feels like the world of math is so vast there’s something for everyone to enjoy casually. That feels like a video game analogy to me with all the different genres built around basic fundamental concepts.