When measuring the observed pressure, density or temperature profiles of the intracluster gas, and hence the mass of clusters of galaxies, projection effects or departures from the spherical symmetry hypothesis may induce biases. In order to estimate how strongly the cluster observed properties depend on the direction of observation, we use a constrained hydrodynamical simulation of Virgo cluster that replicates the actual cluster of galaxies. In this case study, we analyse Virgo properties when they are projected along different directions including along the Milky Way-Virgo axis which mimics our observation direction. We compare the hydrostatic mass and the hydrostatic mass bias from the projection along the different observation directions to that derived from the 3D simulation. We show that projection effects impact the determination of Virgo mass. We particularly demonstrate that the mass and pressure along the line of sight correlates with the 2D and 3D-deprojected electron density and pressure profiles intensity and thus impacts the derived hydrostatic mass. We also show that the deviations to the hydrostatic equilibrium induced by pressure discontinuities within the cluster are emphasized by the deprojection process and thus makes the hydrostatic mass estimation invalid at these radii.