Physics 101, Okay, Im not sure what Im doing wrong. Im using fy, 35cos(45) fx, 35sin(43) Not too sure how to find F. help?

What you have in the diagram is a right triangle, where the fy component intersects the fx component at a 90 deg angle. And that makes F = sqrt(fx^2 + fy^2) the hypotenuse. You best reread about the right triangle and the Pythagorean equation.

So we can employ the trig relationships to find F = fy/sin(theta) = 35/sin(radians(45))) = 4.9497E+01 = 49.5 units. ANS.

But here's where you err. fy, 35cos(45) fx, 35sin(43) are not correct. That 35 is in fact fy = 35 as given. So you really have fy = F sin(theta) to solve for F = fy/sin(theta).

fy = 35 = F*sin(45) = F*sqrt(2)
F = 35/sqrt(2) = (35/2)*sqrt(2) <<<

I don't know what you mean by the commas in "fy, 35cos(45) fx, 35sin(43)"
Here's how I do it.
Fy = 35 = F*sin(45)
Solving for F,
F = 35/sin(45) = 49.5 units long

Additional explanation. I've done so many of these I may have taken too big a jump for you.
sine = opposite / hypotenuse
the opposite is a dotted line -- it is the same length as what the drawing calls Fy. The hypotenuse is F. So
sin(45) = 35/F
Cross-multiplying gets you F*sin45 = 35