Ok, so
We got the next triangle:
We know that ∆CDA ~ ∆CAB ~ ∆DBA. This means that triangles CDA and ADB are congruent.
Knowing this, we could make the next relation applying the geometric mean theorem:

Now, we multiply by cross:
![\begin{gathered} (15)(4)=(x)(x) \\ 60=x^2 \\ \sqrt[]{60}=x \\ 7.7\cong x \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/cl8r0i71r74b16mwdxgexyqll1wm7k0iqa.png)
Finally, x measures 7.7.