Manometer with non linear height change.

[buildingblocs]

I am trying to establish a mathematical relationship between heights h1 and h2 (please refer to figure attached) for a manometer whose RHS channel is the shape of a triangle (defined by a base length and the angle theta). I want to be able to calculate the heights h1 and h2 for a given change to the pressure p1. Any help or a point in the right direction would be much appreciated.

Regards,

ps. This is not an practice question, I am hoping to do this with multiple manometer with various geometries.

 

[buildingblocs]

here is my attempt to get h₁ or h₂ interms of Δh. Anyone know a cleaner way in doing so?