Find value of x, w/o trigo, from triangle with alg. expr. for side lengths, angles

[vseskv]

Hello I have tried to solve this one but no luck.

Find the X.

no trigo is allowed to solve this problem.

I tried to construct a cross angle from b to AC and used the sentence BC/BA=CK/KA (K=the cross angle to AC) and i have tried to use the imagination sentences but couldn't get any link.
pitagoras sentence didn't helped me to unfortunately (after building plumbs to the ribs).

 

[stapel]

Hello I have tried to solve this one but no luck.

Find the X.

Before getting started, I think one would need to know the relationship between "x" and "X".