Find right triangle vertex by 2 vertex, hypotenuse and angles

Question

Trying to solve this problem for 3D. Please, see triangle below.

1. A and C are known vertices - A(x1, y1, z1) and C(x1, y1, z3)
2. Angle ACB is right angle, others are known
3. Distances AB and AC are known too
4. x and y coordinates are the same for A and B
5. z coordinate is the same for B and C
6. We need to find vertex B(x2, y2, z3)

I will appreciate for any help!

Triangle

Answer 1

The answer is not unique.

$$(x_1+a\cos \theta, y_1+a\sin \theta,z_3)$$

is a solution for any $\theta$, where $a=\sqrt{c^2-b^2}$ is known.