Determine the pressure difference.

To calculate the height of the plane, we use the principle that the pressure difference between two points in a fluid column is given by $\Delta P = \rho g h$. In this case, the pressure difference is due to the column of air between the ground and the plane. This pressure difference is also measured by the difference in mercury column heights.

Step 1: Determine the pressure difference.
The pressure at the ground ($P_{ground}$) is 75 cm of Hg.
The pressure at the plane ($P_{plane}$) is 63 cm of Hg.
The pressure difference ($\Delta P$) is:

$$$$