Problem $5$

The manometer shown contains three immiscible liquids with densities ${}_A=600k\frac{g}{m^3},{}_B=1600k\frac{g}{m^3},$ and ${}_C=900k\frac{g}{m^3}.$ The liquid heights and angles $($measured from the vertical$)$ are shown in the diagram. One end of the manometer is open to atmospheric pressure air. The other end is capped and contains air of unknown pressure, $P_1.$ What is the gage pressure $P_1?$