  A number of ongoing surveys are likely to discover star-black hole binaries
in our Galaxy in the near future. A fraction of them may be triple systems
comprising an inner binary, instead of a single black hole, which might be
progenitors of binary black holes (BBHs) routinely discovered now from the
gravitational wave. We extend our previous proposal to locate inner BBHs from
the short-term radial-velocity (RV) variation of a tertiary star in coplanar
triples, and we consider noncoplanar triples and their long-term RV variations
as well. Specifically, we assume coplanar and noncoplanar triples with an inner
BBH of the total mass $20~M_\odot$, whose outer and inner orbital periods are
80 days and 10 days, respectively. We perform a series of N-body simulations
and compare the results with analytic approximate solutions based on quadrupole
perturbation theory. For coplanar triples, the pericenter shift of the outer
star can be used to detect the hidden inner BBH. For noncoplanar triples, the
total RV semi-amplitude of the outer star is modulated periodically on the
order of $100$km/s due to its precession over roughly the Kozai-Lidov
oscillation timescale. Such long-term modulations would be detectable within a
decade, independent of the short-term RV variations on the order of of $100$
m/s at roughly twice the orbital frequency of the inner binary. Thus the RV
monitoring of future star-black hole binary candidates offers a promising
method for searching for their inner hidden BBHs in optical bands.
