Maths - it could happen to you.

So - what I'm trying to say here (in this long winded introduction), is that the last time I did trigonometry I had a spiked haircut (short on top, long at the back) and Australia had not yet celebrated its bicentennial.  In fact when I closed my answer booklet at the end of the HSC maths exam (2nd time around) I probably thought that my troubled relationship with Sines, Cosines, Quadratic Equations and the rest of the trigonometric palarva was over..

But here we are 30 years later, and my current woodworking project involves making a frame for a mirror.  A circular mirror. And the frame is made up of lots (35) bits of wood pointing outwards.  Like that sketch below

So to work out how to cut these peices of wood so they fit nicely (or nice-enoughly) together, I've had to pull some maths out of the dusty reaches of my brain and work out some angles.  Using Pi, tan, and arctan.  Thank goodness the internet has sprung up since I solved my last trig problem - not that it could solve the problem for me, but it could remind me of the tools I could use to do it. If you're interested,  I worked out the outside diameter and then the inside diameter.  Turning the inside into a percentage of the outside, I could work out how much length each piece would need to 'cut in' on either side.  What I really wanted was the angle to put my dropsaw onto though. So using my two values I used a tan equation (I had adjacent and opposite lengths).  From there it was a matter of using arctan to determine what the angle was. Therefore the angle to set my dropsaw was 90 minus the value I'd found.   Phew!

And did it work? Yeah - pretty much. It was a bit of a pain that I had about 7 different widths of wood - so I had to repeat the calculation each time - if I hadn't chucked out my scientific calculator all those years ago I would have used it so I could just plug in the lengths.  Of course calculating the angle down to two decimal points wasn't all that useful, as the drop saw only really had 1 degree settings, but I could at least eyeball an approximate setting.  It wasn't perfect, but it wasn't too bad.  I'm sure the imperfectness of my woodworking skills that I'll be using to complete this project will far outweigh any errors I've made in my calculations and cutting.