You'll use the sine trig function because we want to tie together the known opposite side (10) and the unknown hypotenuse (x).
sin(angle) = opposite/hypotenuse
sin(55) = 10/x
x*sin(55) = 10
x = 10/sin(55)
x = 12.2077 ... make sure your calculator is in degree mode
x = 12.2
Answer: Choice A