Anonymous

# Solve using the Law of Cosines?

This is the problem: http://i3.photobucket.com/albums/y74/Okimo/number1...

I cannot figure out what I'm doing wrong.

Update:

Oh! My bad. I didn't even realize I left out what was what.

a=25

b=35

c=?

d=?

theta=?

and the other greek symbol = 120

Update 2:

Oh! My bad. I didn't even realize I left out what was what.

a=25

b=35

c=?

d=?

theta=?

and the other greek symbol = 120

Yes, it is given to be a parallelogram.

Relevance
• Anonymous

Is it safe to assume that the whole outer structure is a parallelogram?

Source(s): EDIT: Nevermind; Kathleen B beat me to asking this.

Being a parallelogram makes this much easier.

We will find the entire length of each of the two diagonals, helpful because we know the diagonals of a parallelogram bisect each other..

I am going to call the diagonal of which c is a part, X (X = 2c)

And the diagonal of which d is a part, Y (Y = 2d).

You may recall that consecutive angles in a parallelogram are supplementary, so Ө = 60°.

X² = 25² + 35² - 2*25*35*cos120

X² = 25² + 35² - 2*25*35*(-1/2)

X² = 25² + 35² +25*35

X=52.2

thus c = 52.2/2 = 26.1

Y² = 25² + 35² - 2*25*35*(1/2)

Y² = 25² + 35² -25*35

Y = 31.22

thus d = 31.22/2 = 15.61