Find The Missing Values Within The Parallelogram

(as seen in the picture below)

Question

Find The Missing Values Within The Parallelogram

(as seen in the picture below)

anonymous · Answer

|dw:1384927056662:dw|

I will try to fill in some of the missing information in the next drawing, please tell me if I'm correct.  (a = 5, b = 8, theta = 45 degrees.  Find sides c, d, and phi.  

|dw:1384927192354:dw|

Looking at the bottom triangle, with sides [x], b, and d:

|dw:1384927457603:dw|

Again, I don't know if the data I filled in so far is right.  The answers should come out to be:

a = 5 (given), b = 8 (given), c = 12.07, d = 5.69, theta = 45 degrees (given), phi = 135 degrees.  

In the pictures, I forgot to label phi as 135 degrees.  (180-45) [degrees].