find a relationship between angles a & y from the given picture

i'm trying to find a relationship between angles a & y given in the picture. 'a' should be the input (i.e. its value is known) and 'y' is the desired variable to be found. the equation should be solvable in matlab.

[Star Strider]

I looked at this earlier, and the problem is that there is no way to determine what ‘a’ is referenced to. The centre line appears to be an extension of the line that defines ‘y’, but ‘a’ is completely ambiguous.

[Image Analyst]

Well it's obvious that a+x=y, so that's the relationship.

But I doubt it's as simple as that. That's so trivial that I'm wondering what the homework question is really after. For example, maybe the circle is a droplet of liquid and has some index of refraction so that the centerline is not a straightline extension of a beam of light emanating from the origin. But then you'd need to know the index of refraction, but once you have that you can find virtually anything else that you want. Or maybe the stuff outside the circle has some kind of dispersion and the spread (2x) depends on how cloudy the material is. Who knows? Not us.

[Star Strider]

The lowest line does not appear to go through the origin (lower right corner), and does not appear to be referenced to anything else. So if the figure’s drawn accurately, ‘a’ is indeterminate from the information provided. That’s the problem I’m having with it.

Answer 1

[Image Analyst]

Are there any restrictions on how you solve this - what functions you use? Or do you just need the answer? Because it's obviously trivial if you can use certain functions. Here's just two methods

1. use ginput(2) to have use click on line
2. use atan2d() to get the angles.

or

1. use rbbox() or imrect() to draw a box around the line you want.
2. use imcrop() to crop it.
3. threshold and use polyfit to get the slope of the line.