A detailed theoretical examination of the jump conditions of the bow shcok in an ideal magnetohydrodynamic flow pattern is used to obtain two sets of approximate analytic representations of the parameters behind the bow shock. From these analytic representations contour maps can be drawn to show clearly the influence of the solar wind magnetic fields, especially their directions on these parameters. We next use these results to examine the expected thickness of the magnetosheath. In order to obtain an analytical solution that is tractable we assume that the average values of the parameters along the radial direction in the magnetosheath are simply equal to their values just behind the bow shock. We emphasize that this assumption allows variations of these parameters along the radial direction. A very simple approximate formula for the thickness of the magnetosheath is obtained which satisfies the boundary conditions and conservation laws of mass and momentum flux. Two years magnetometer data from the Isee satellite crossing the magnetosheath during the period between October 1977 to October 1979 are used to determine empirically the thickness of the magnetosheath and to compare these observed thickness with theoretical estimates. Because of the sensitive dependence of the formula for the magnetosheath thickness on the value of &ggr;, the polytropic exponent of the plasma gas, we can use this comparison to determine the optimum value of &ggr;. A value of &ggr; = 2 gives much better agreement than 3, 5/3 or 7/5.