Abcd is a parallelogram. its diagonal, ac, is 18 inches long and forms a 20° angle with the base of the parallelogram. angle abc is 130°. what is the length of the parallelogram’s base, ab?

The diagonal AC, along with the base AB and length BC, forms a triangle. The triangle's dimensions are:
AC = 18
∠CAB = 20°
AB = ?
∠ABC = 130°
BC = ?
∠BCA = 180 - 20 - 130 = 30°

Thus, we may apply the sine rule:
sin(BCA) / AB = sin(ABC) / AC
AB = sin(30) * 18 / sin(130)
AB = 11.7 inches