How Is the Net Force on Earth Calculated When Aligned with the Moon and Sun?

[SoccaCrazy24]

When the Earth, Moon, and Sun form a right triangle with the Earth located at the right angle, the Moon is approaching its third quarter. (The Earth is viewed here from above its north pole.) Find the magnitude of the net force exerted on the Earth.

Well I found the gravitational force of the Earth on the sun to be 3.54x10^33 and the gravitational force of the moon the Earth to be 1.98x10^31. To find the net force would i just add the two together or subtract the two? or would i use pythagorean's thm... a^2 + b^2 = c^2 ? If you need me to show the work i got for the gravitational forces please let me know...

 

[Chi Meson]

Since these two forces are vectors, and since they are not colinear (pointing is the same or opposite directions) then you must add them as vectors. When vectors are at right angles (such as they are, then using the pythagorean theorem is the easiest way of finding the magnitude of the vector sum.