Question

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?

Answer 1

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

Explanation:

Answer 2

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