A football is kicked at ground level with a speed of 20.8m/s at an angle of 23.3 degress to the horizontal. How much later, in seconds, does it hit the ground?

Tf =(-20.8m/s x Sin 23.3)/-9.80m/s^2
=0.839s

this doesn't sound right to me

h(t)=h(0)+vvt-1/2 g t^2

0=0+20.8sin23.3 t - 4.9t^2
t=0, t=20.8sin23.3/4.9

so your denominator is wrong.