In a triangle ABC, the angle AC = 6√3 B = 60 (degrees) A = 45 (degrees). Find: BC.

Given:
AC = 6√3 cm
∠B = 60 °
∠A = 45 °

To find:
BC -?

1) To solve the problem, it is necessary to use the theorem of sines (in a triangle, the sides are proportional to the sines of the opposite angles):
AC / sin B = BC / sin A;
2) Substitute the known values into the formula:
6√3 / sin 60 = BC / sin 45;
3) Use the sine table to determine the values of the known angles:
6√3 / √3 / 2 = BC / √2 / 2;
4) Calculate the side BC:
BC = 6√2 (cm).

Answer: BC is equal to 6√2 cm.