Answer
The magnitude of the net force on the moon is $4.77\times10^{20}N$.
Work Step by Step
1) Calculate the gravitational force $F_{SM}$
We have mass of the sun $M_S=1.99\times10^{30}kg$, mass of the moon $M_M=7.35\times10^{22}kg$, the distance between them $r_{SM}=1.5\times10^{11}m$ and constant $G=6.67\times10^{-11}Nm^2/kg^2$
$$F_{SM}=G\frac{M_SM_M}{r_{SM}}=4.34\times10^{20}N$$
2) Calculate the gravitational force $F_{EM}$
We have mass of the earth $M_E=5.98\times10^{24}kg$, mass of the moon $M_M=7.35\times10^{22}kg$, the distance between them $r_{EM}=3.85\times10^{8}m$ and constant $G=6.67\times10^{-11}Nm^2/kg^2$
$$F_{EM}=G\frac{M_EM_M}{r_{EM}}=1.98\times10^{20}N$$
3) As these two forces are perpendicular, the magnitude of the net force on the moon is $$\sum F=\sqrt{F_{SM}^2+F_{EM}^2}=4.77\times10^{20}N$$
