I have the following problem where I need to find out the missing the angle. I have to apply some triangulation method to solve.

I have the values of the hypotenuse.
My solution is to break this triangle into its base and perpendicular considering that 90 degrees is opposite the hypotenuse get the remaining to angles. Is that method correct?
Also the angle x which I have to find is changing with time. How can I incorporate the time changing element.
Edit with new figure
I have the lengths a and b and I need to find x. My plan is to find the other two angles using the triangles and subtract those to find x.