I've read what you wrote at least 20 times, as best I can tell your trying to lead me to:
4/X = C/10
This isn't a homework problem it's just something I run into on construction jobs often. I think your trying to get me to figure it out, but I guess I have holes in my education preventing me...
Sure, the two triangles in the first diagram are similar. But with only one known value for both, (4 ,10) I know of no way to derive the length of c.
I'm not sure what "extract he roots of quartic" means.
1. I'm looking for the value of "C". All starting information is in the first attachment.
2. Formulas needed are believed to be Pythagoras theorem and trigonometry.
3. "The attempt at a solution": This would be the second attachment. I've wracked my brain for hours and have come to...