find the point two lines intersect in 3d with a mixture of cartesian and spherical coordinate system knowns

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I have line 1:

  • originating from origin (0,0,0) and magnitude (length) of 7

I have line 2:

  • originating from a shifted position (0, 0, 0.4) and the polar and azimuth are also known (see picture)

I am trying to determine the length of line 2 when it intersects the end of line 1. Do I have enough knowns to do this? See attached where I tried to find a triangle and law of sines but can't seem to find the angle I need in the triangle enter image description here