AB = 6√3, BC = 6, angle CAB = 30 degrees. Find the angle B and C.

Let us determine what the sine of the angle C will equal if from the condition of this problem we know that the length of the BC side is 6, and the length of the AB side is 6√3:

sin 30 ° / BC = sin C / AB;

sin C = 6√3 * 1/2: 6 = √3 / 2.

The value of this sine corresponds to an angle of 60 °.

Let us determine what angle B will equal in this case, because as we know from the school curriculum, the sum of the angles of the triangle is 180 °:

180 – 60 – 30 = 90.

Answer: With such initial data, the angle C will be equal to 60 °, and the angle C will be equal to 90 °.