roflmao, yes, you had Z correct, if the LENGTHS were correct - but your angles were wrong in that case.
*edit*
Give me a minute, I'll work it all out. You need X and Y, correct values, right?
Z = 4.9244289"
Bottom inside angle of the triangle = 23.9625 degrees ( = arccos(4.5/4.9244289) in radians)
Upper inside angle of the triangle = 66.0375 degrees ( = 180-90-23.9625)
Of course, now our lower triangle's measurements are f'd up.
Upper angle of the lower triangle = 23.9625 degrees ( = alternating interior angles of two parallel lines)
What about the other two angles of the lower triangle? Well, let's take a look at the LOWEST triangle.
If you extend the line segment forming the vertical of the right angle in the upper right quadrant, down to the bottom of the diagram, you find that you have a 35-90-55 degree triangle. Again, using Alternate Interior Angles, we find that the former 100 degree angle is in fact 125 degrees (180-55)
Thus, our lower triangle is a 23.9625 - 125 - 31.0375 triangle, in degrees.
Now back to our Law of Sines
X / (sin31.0375) = 4.9244289 / (sin125)
X = 3.09958393"
Y / (sin23.9625) = 4.9244289 / (sin125)
Y = 2.44155023"
This makes sense, since you are saying that your upper horizontal is 2.0", and you have a 35 degree incline, you'd expect about a 2.4" measurement there.
Anything I miss?
*edit* Just a small aside, things like this are why I cracked up laughing when I read a friend's fanfic of FF7. It was Cid Highwind (the engineer) yelling to another that they needed "Trigonometry and an ass-kicking!"