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Originally Posted by Hitman
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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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Yes, thats true. The equation involves a trig function, so obviously the relationship would be a curve, silly me.
Here's the equation that the card used. The Trebelle basically estimated the answers for this:
inverse Tangent of (
distance sub traveled /
range difference). There are extenuating circumstances, but thats the basic idea.