Solving for the Height of Mercury: Is This Equation Correct?

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The discussion centers on the calculation of mercury height using the equation P_gauge = ρ_air·g·h_air + ρ_Hg·g·h_Hg, with a given gauge pressure of 3.75 KPa. The user calculates h_Hg to be 2.8 cm but doubts the accuracy of this result. They seek confirmation on whether the equation used is appropriate for this problem. The conversation emphasizes the need for clarity on the correct application of fluid statics principles. Ultimately, the user is looking for assistance in verifying their calculations and understanding the equation's validity.
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Homework Statement

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The attempt at a solution

To find the height of mercury I have used the following equation:

P _{gauge}=\rho _{air}\cdot g\cdot h_{air}+\rho _{Hg}\cdot g\cdot h_{Hg}

where P _{gauge}=3.75 KPa

So I solve for h_{Hg} and get 2.8 cm. I don't think this is correct. Am I even using the correct equation?
 
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