How do you determine the dissociation constant of a weak acid when you only have the pH and H3O?

pH = 3.78

Conc H3O = 1.6e-4

right so the dissociation constant of a weak acid that follows the following equasion:
                    HA + H2O ----> H3O + A-

is Ka = [H3O][A]/[HA]

we also know that pH is:
                                       pH = -log[H3O]
                                       
so we can work out the H3O from the pH even if you didn't have it to start with.

now you have your [h3O], but since this acid is monoprotic, ie it only gives off one proton when it disassociates. that mean that for evey hydrogen(h3O) created there has to be an equal ammount of the counterpart A- created

therefore [A-] = [hco3]

so your Ka becomes:

Ka = [x^2]/[HA]