  We present the results of a study of the type II Cepheid ($P_{puls} = 4.974
d$) in the eclipsing binary system OGLE-LMC-T2CEP-098 ($P_{orb} = 397.2 d$).
The Cepheid belongs to the peculiar W Vir group, for which the evolutionary
status is virtually unknown. It is the first single-lined system with a
pulsating component analyzed using the method developed by Pilecki et al.
(2013). We show that the presence of a pulsator makes it possible to derive
accurate physical parameters of the stars even if radial velocities can be
measured for only one of the components. We have used four different methods to
limit and estimate the physical parameters, eventually obtaining precise
results by combining pulsation theory with the spectroscopic and photometric
solutions. The Cepheid radius, mass and temperature are $25.3 \pm 0.2 R_\odot$,
$1.51 \pm 0.09 M_\odot$ and $5300 \pm 100 K$, respectively, while its companion
has similar size ($26.3 R_\odot$), but is more massive ($6.8 M_\odot$) and
hotter ($9500 K$). Our best estimate for the p-factor of the Cepheid is $1.30
\pm 0.03$. The mass, position on the period-luminosity diagram, and pulsation
amplitude indicate that the pulsating component is very similar to the
Anomalous Cepheids, although it has a much longer period and is redder in
color. The very unusual combination of the components suggest that the system
has passed through a mass transfer phase in its evolution. More complicated
internal structure would then explain its peculiarity.
