I'm quiet a newbie in maths (it's decades since high school), and I need your help for a research I'm doing for my PhD.
That's the situation: UNDER IDEAL CONDITIONS I have a semicircle with horizontal diameter (like a dome, to understand), and a vertical line crossing the diameter (on the right of the center of the circle). I already have a formula to calculate the portion of the diameter on the right side of the vertical line (as a ratio of the whole diameter), whic is MP = A/B *100, where A is the portion of the diameter on the right side of the vertical line and B is the whole diameter.
Unluckly, UNDER REAL CONDITIONS the semicircle is quiet always rotated counterclockwisly around its center (let's call alpha the rotation angle), while the original vertical line doesn't change. To make the same calculations, i need to draw a new vertical line passing thru the right-most end of the semicircle, and a vertical line passing thru the left-most point of the semicircle (which is no more the end of the diameter because of rotation), so the formula becomes MP' = A' / B' * 100, where A' is the horizontal distance bewteen the two right-most vertical lines and B' is the distance between the right-most and the left-most vertical lines.
I hope the situation is clear; now that's my question: IS THERE ANY FORMULA TO CALCULATE MP AS A FUNCTION OF A', B' AND ALPHA? I guess I need trigonometrics...**
Hope you can understand the question; thank you so much in advance to anyone will answer and help me.
AP