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Basically, this chart doesn’t use Sin curves at all. I just says that, if a=b, then AOB has to be 45deg, because we have a standard right triangle with two equal legs.
This chart asks you to figure out the values for (a) and (b), then simply shows you their ratio. If the ratio is 1:1, then the angle is 45deg. If the ratio is a little bit less, then the angle decreases by an equivalent amount. If the ratio is more, well it increases by the same amount. This is a very neat way to figure AOB, in my opinion.
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Thanks for your explanation
However, I *think* you do have to use the Sine at one point for doing it with an equation: The proportion 1:1 is only correct for the 45º angle, but if my thoughts are right, the rest of the angles will not follow a linear or aritmetical proportion (F.e. a proportion of 70% height vs. length is NOT 70º AOB but rather 45º) but instead a sine curve one:hmm: Am I right?
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Interestingly, if you want to find their speed, just use the Pythagorean Theorem to find the distance traveled (c), divide by seconds, and multiply by 1.777. No messy business with Sin curves or anything like that.
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Yup good catch
Though it can be also determined with Sines, of course. Interestingly, the quickest method is very different when using a slide ruler or pure algebra. With a Slide Ruler using Sine is way faster, while you are completely right in that using just algebra solving the problem with Sines would be an unnecessary waste of time.
But that's the lovely part of maths: Many times you can do the same thing by different ways
and you can then choose which ones fits better your real purpose
