 Hey guys, this is Alex. This video is actually on trigonometry, so if you're not interested, you know, go ahead and give me a thumbs up anyway and move on to something else. But it's actually about repairing this tool here, this is a sterret pocket scribe. It used to have a much longer finer point on it, which I managed to break within about 15 minutes of having it. I'm a little disappointed about that, but I think it was my fault for using it at the wrong angle. I've re-grounded it to a point just to be able to still use it, but I wanted to figure out what the original point was, what the original angle was, so that I can make it whole again. I had kept the little part that broke off, I found it and hung on to it, and I've lost it now, but that's okay because I've memorialized it. So what I did was I took a photograph of it, and I may show you that there may be an image that comes up, but this is the, got it upside down, this is the image having made it negative and gotten rid of the color and enhanced it a little bit, blown it up. But you can see the point, and it's not as sharp as you might like, but whatever. And so I knew from trigonometry that if I can process this as a triangle, then I can compute what this angle is here, and then when I re-grind it, I can shoot for the correct thing. So I took this piece of paper and I marked with the scribe, actually the three points that I drew from using a rule, and made that a right angle, so now we have a right triangle and we can use our normal rules of trigonometry. And so here is the resulting computations. Here are the resulting computations. Okay, so here's our triangle. I flipped it around, but I want this included angle here, okay? So I measured this with my little, my new metric steric ruler here, or scale, and so all these numbers are in millimeters, and these are the values that I got. So we have a right triangle, and let's just call this A, B, and C, okay, traditionally. The first thing I did was I wanted to make sure that these numbers made sense, that I hadn't measured something wrong. So I used the Pythagorean theorem, A squared plus B squared equals C squared. So some of the squares of the two sides should be equal to the square of the hypotenuse. That gives you this formula, and it turns out that, or this expression, turns out I was within 20 or 30 there, so I considered that close enough for my purposes. So then I want to compute theta. So what I did was I used the three basic trig functions, tan, sine, and cosine. And so these are the ratios that you get. So tan is opposite over adjacent, sine is opposite over hypotenuse, and cosine is adjacent over hypotenuse. So I want to sort of, you know, amortize the error across three different computations to just make sure that, you know, everything made sense. Okay, so you get these results, 14.82, from the tangent, so you take the inverse tangent of this value to solve for theta, 14.82, for the sine I get 14.75, and for the cosine I get 15.79, and so all you need is a scientific calculator, or actually a Windows calculator will do it for you. You put it into scientific mode. So my original guess was 15 degrees, and these three values largely confirm that guess. But just to sort of see what the error was, I computed an average. So that's just the sum of those three numbers divided by three, 15.11 with a standard deviation of .46 degrees. This should say degrees here, but that's okay. And so I conclude that it's close enough to 15 degrees, that I can use that as a target for re-grinding the little tip of this thing. It's currently at about probably 30, 35 degrees, something like that. So anyway, the point was not so much about the scribe, but about that trigonometry is actually useful for something. And if you remember the stuff from high school occasionally, you may be able to do something with it that is helpful. So anyhow, thanks for watching. Have fun. Just keep it legal. And if you have any questions, add them to the comments or send me a note. All right. Cheers.