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

Answer: 11.7

Explanation:

Answer 2

This is the concept of geometry, to solve for the long base of the parallelogram we use sine rule which states that, given triangle ABC with sides a,b and c
then
a/sin A=b/sin B=c/sin C
From our question, ABC=130, thus b=18 in
BAC=30, the length of the base will be a
thus;
a/sin 30=18/sin 130
a=(18sin 30)/sin 130
a=9/0.7660
a=11.75 inches

The base is therefore 11.75 inches