Given: triangle ABC Angle A = 60 degrees. Angle C = 75 side BC = Find AC.

The angles of a triangle add up to 180 °
Therefore, to find angle B, subtract angle A and angle C from 180 ° (180 ° – 60 ° – 75 °)
Angle B = 45 °

Next, we apply the theorem of sines (the sides of a triangle are proportional to the sines of the opposite angles) a / sin A = b / sin B = c / sin C

Substitute the data from the condition -> BC / sin 45 ° = AC / sin 60 °.
AC = 3 √ 6 * sin 60 ° / sin 45 °
AC = 9