1. Using triangle ACD calculate the length AC.

2. Calculate the size of angle ABC

For triangle ACD you know two sides (a and c) and the angle (D) opposite the unknown side (d), you need an equation that relates these quantities. That would be the Law of Cosines: \(\displaystyle d^2=a^2+c^2-2ac*cos(D)\). Note that \(\displaystyle cos(60^o)=\frac{1}{2}\).

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: \(\displaystyle \frac{sin(A)}{a}=\frac{sin(B)}{b}\). Solve this for \(\displaystyle sin(B)\) (note that \(\displaystyle sin(30^o)=\frac{1}{2}\)), then use the inverse sine (also known as arcsin) to get angle B.