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?

8.0 in
11.7 in
27.6 in
40.3 in

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?



8.0 in
11.7 in
27.6 in
40.3 in

anonymous · Answer

https://gmcprep.owschools.com/media/g_geo_ccss_2014/11/geo_10_a_16_assess_media_7.gif

anonymous · Answer

@pooja195

anonymous · Answer

@rhr12

anonymous · Answer

@wolf1728

rhr12 · Answer

do you know the area of the parallelogram?

wolf1728 · Answer

We can say that the half angle located at the upper right would be 30 degrees.
We have 2 angles and an included side so we can use the Law of Sines

rhr12 · Answer

we can eliminate 40 and 26. the confusion is 8 or 11.7.

wolf1728 · Answer

I drew a new diagram

anonymous · Answer

11.7?

rhr12 · Answer

11.7 i guess

anonymous · Answer

thats ehat i had first but i wasnt ture so i asked yall

rhr12 · Answer

is that wrong? I had never did something like that. MAybe @wolf1728  will take you to the end

wolf1728 · Answer

Angle B is 130 degrees
side b is 18 inches
Angle C is 30 degrees
side C = (sin(C) * b)/sin B

side C = .5 * 18 / 0.76604

side C = 11.7487337476

wolf1728 · Answer

Well I guess it is 11.7 and you've got the proof right there!
:-)