Finding net gravitational force magnitude on moon

[TmrK]

Homework Statement

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force that the sun exerts on the moon is perpendicular to the force that the Earth exerts on the moon. The masses are: mass of sun=1.99 × 1030 kg, mass of earth=5.98 × 1024 kg, mass of moon=7.35 × 1022 kg. The distances shown in the drawing are rSM = 1.50 × 1011 m and rEM = 3.85 × 108 m. Determine the magnitude of the net gravitational force on the moon.

Homework Equations

F_sm=Gm_sm_m/r_sm²
F_em=Gm_em_m/r_em²
F_net=F_sm+F_em

The Attempt at a Solution

Solved for Fsm, which equals to 4.3359444667x10⁶⁴
Fem=1.977847934X10⁸⁴

After finding the sum of these two forces, which is 8.68x10¹²⁸, I decided to find the square root of this and ended up getting 2.946183972531247x10⁶⁴.

This, however, was proven incorrect.

 

[cepheid]

The forces aren't in the same direction, so you can't just add their magnitudes together. You need to find their vector sum.

EDIT: Also you should really include units in all of your calculations.

 

[TmrK]

Homework Statement

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force that the sun exerts on the moon is perpendicular to the force that the Earth exerts on the moon. The masses are: mass of sun=1.99 × 1030 kg, mass of earth=5.98 × 1024 kg, mass of moon=7.35 × 1022 kg. The distances shown in the drawing are rSM = 1.50 × 1011 m and rEM = 3.85 × 108 m. Determine the magnitude of the net gravitational force on the moon.

Homework Equations

F_sm=Gm_sm_m/r_sm²
F_em=Gm_em_m/r_em²
F_net=F_sm+F_em

The Attempt at a Solution

Solved for Fsm, which equals to 4.3359444667x10⁶⁴N
Fem=1.977847934X10⁸⁴N

After finding the sum of these two forces, which is 8.68x10¹²⁸N, I decided to find the square root of this and ended up getting 2.946183972531247x10⁶⁴N.

This, however, was proven incorrect.

Edit: did try finding it by vector sum, but did not worked as well. I'm not going to post what number I ended up with.
It's that, or WileyPlus's system...