Would one F in a cl ruin your chances of going to a college like Washington?

Im having a tough time in my Trigonometry cl and I might not be able to p it. I have never gotten below a B in a cl before and my high school GPA is somewhere between 3.6-3.8. My SAT scores should be very high being i got a 1750 on the PSAT. Im also taking Trig. as a junior, making it an honors level cl along with three AP courses. If I did fail this cl, would it ruin my chances of going to University of Washington, which is the school I want to attend the most. Your opinions would be much appreciated.