I asked the same question some time ago, but it is closed. This time I will be clearer (I hope).
If I have a right triangle $c ^ 2 = a ^ 2 + b ^ 2$, and $b > a$ (so $a$ is the shorter side and $b$ is the longer side). Now, put a right triangle in a semi-circle with the hypotenuse is equal to the diameter, $((a * 4) - (a * b / c)) / 3$ ~ circle arc $a$.
For example if have right triangle $10 ^ 2 = 5 ^ 2 + (8,6602\dots)^ 2$ which was placed in a semi-circle with a diameter of $10$, will obtain $((5 * 4) - (5 * 8,6602\dots / 10)) / 3 = 5,223\dots \sim 5,235\dots$.
In this example 5,235.. is the length of circle arc with the same angle as the right triangle side of 5, in this case it is obvious angle of 60 degrees (viewed from the center of the semi- circle).
Another example if have a right triangle $10 ^ 2 = (7,07106\dots)^ 2 + (7,07106\dots)^2$, will obtain $((7,07106\dots* 4) - (7,07106\dots* 7,07106\dots/ 10)) / 3 = 7,761 \sim 7,853\dots$. In this case $7,853\dots$ obvious is the length of 1/4 circumference, or, circle arc of 90 degrees (viewed from the center of the semi-circle).
So question is, whether formula $((a * 4) - (a * b / c)) / 3$, used before in this or some other form ? (question is important because this formula can be improved (with a lot of manipulation) to give a much smaller error) Srbin
EDIT (M.S): This picture was not posted by OP, I've added it since it might help to clarify the question.