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Say you have a right triangle, you know the length of the 2 sides of the 90 degree corner (so you know everything, the hypotenuse and all 3 angles). Inside this triangle, you draw a line (not the height) so you create 2 new (non-similar) triangles: 1 new right triangle and another one.

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Is there something that the original big right triangle (ABD) and the new smaller triangle (ABC) have in common? I am looking for a ratio that stays constant, using some property of both triangles: angles, surface, circumference, inside circle ratio, height,... I.e. the ratio of some function of alpha / (AC/AE) = that function of beta / (AD/AF), something like that, or BC/BD= ...* some function (alpha/Beta), or ... I've looked at http://en.wikipedia.org/wiki/Right_triangle, but it's not clear to me. Thanks for the help!

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    $C$ can be any point on $BD$ and you can draw a diagram which works. The two triangles have side in common and are both right-angled. AB/AB=1. It would help to have some motivation for the question - why do you think there might be something the same?2012-08-23
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    If you throw in $\alpha$ and $\beta$, there is a large number of relationships. One can produce a few without mentioning angles. There seems to be no point in producing a random list without knowing what the aim is.2012-08-23
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    Hi André, thanks for responding. The aim is to use this in a filter, and I need to be able to treat a variety of movements of a variable in the same way: it doesn't matter to this filter how high the variable goes up, so I must calculate something from a reference point that allows me to classify all these moves in the same category so I can ignore the difference in vertical movement. For this, I need to compare the previous movement with the current movement, and if the "ratio" that I want to calculate stays the same, then I don't need to adjust anything.2012-08-23

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