I'm not sure, but you might be over-complicating this part.
If you need "b" to be a fixed length (1.300") and the triangle has a right angle, you should be able to handle everything with relations instead of equations.
Here is a quick & dirty sketch (fully defined)
The 1.300" line has a perpendicular relation to the angled line, and it will update accordingly when you change all of the other numbers.
Not sure if this is what you are after, but this is what it sounded like to me.
Thank you for your reply. I know that the relationship will update in SolidWorks as the other dimensions change due to their relationships. I need the resulting dimension of the short leg to deduct it from the overall length of a rail. I just realized that I can solve for the angle B in the large triangle so now I know one side and one angle to put in the formula. a= cot(asin (142/163)) x 1.3.
What I was hoping to do is just grab the dimension of a instead of doing the trigonometry functions.