I was involved in a car accident this weekend and I think I'm innocent.
I pulled up to a stop sign- checked traffic in both directions- saw nothing and proceeded through the intersection. Half way through, a fast moving car came into the intersection. I gassed it to get through asap but the girl in the other car clipped the back end of my car.
She stopped, got out and came over to me and apologized profusely and said " I'm f... ed, I just had 3 beers. The police came , did their investigation and charged her with dui but gave a me ticket for failure to yield- essentially making me responsible for the crash.
Here's why I think I'm innocent- there's a hill just before the intersection that blinds the driver to oncoming traffic.

I went back the next day with a stop watch and measuring tape. At 30 mph ( the posted speed) it takes about 11-12 seconds for a car to get to the intersection from the point on the hill where you can see oncoming traffic. It only takes 4 seconds to get through the intersection- plenty of time unless the oncoming vehicle is speeding. I did my calculations and figured her speed to be 65- 80 mph.
How can I yield to a vehicle that was never in my sight?

Any thoughts- should I fight this or just suck it up and go on?