1. Using triangle ACD calculate the length AC.
2. Calculate the size of angle ABC
After that, look at triangle ABC. You now know two sides (a and b), one of which is opposite your unknown angle (B) one of which is opposite a known angle (A). The equation that relates these quantities is the Law of Sines: . Solve this for (note that ), then use the inverse sine (also known as arcsin) to get angle B.