see the modified diagram below. Note that AB = E + F, where E and F are the bases of the two right-triangles we've constructed. we can find their lengths using trig ratios:

EDIT: i forgot about finding the angle CAD. Note that you can find the length of BC in the same way we found AB. once that is found, we can use Pythagoras' theorem to find the length AC. Thus we will know the lengths of all the sides of triangle ACD, and we can use the law of cosines to find any angle in that triangle we want.