Dihadron azimuthal correlations containing a high transverse momentum ($p_T$)
trigger particle are sensitive to the properties of the nuclear medium created
at RHIC through the strong interactions occurring between the traversing parton
and the medium, i.e. jet-quenching. Previous measurements revealed a strong
modification to dihadron azimuthal correlations in Au+Au collisions with
respect to p+p and d+Au collisions. The modification increases with the
collision centrality, suggesting a path-length or energy density dependence to
the jet-quenching effect. This paper reports STAR measurements of dihadron
azimuthal correlations in mid-central (20-60%) Au+Au collisions at
$\sqrt{s_{_{\rm NN}}}=200$ GeV as a function of the trigger particle's
azimuthal angle relative to the event plane, $\phi_s=|\phi_t-\psi_{\rm EP}|$.
The azimuthal correlation is studied as a function of both the trigger and
associated particle $p_T$. The subtractions of the combinatorial background and
anisotropic flow, assuming Zero Yield At Minimum (ZYAM), are described. The
correlation results are first discussed with subtraction of the even harmonic
(elliptic and quadrangular) flow backgrounds. The away-side correlation is
strongly modified, and the modification varies with $\phi_s$, with a
double-peak structure for out-of-plane trigger particles. The near-side ridge
(long range pseudo-rapidity $\Delta\eta$ correlation) appears to drop with
increasing $\phi_s$ while the jet-like component remains approximately
constant. The correlation functions are further studied with subtraction of odd
harmonic triangular flow background arising from fluctuations. It is found that
the triangular flow, while responsible for the majority of the amplitudes, is
not sufficient to explain the $\phi_s$-dependence of the ridge or the away-side
double-peak structure. ...