Question

A force of 20 N acts toward the east. Another force of 27 N acts at the same point toward the west. What is the magnitude and direction of a third force that produces a resultant of 10 N toward the east?

Answer 1

Since we are working in one dimension (left right or East West), we don't need to worry about angles! It's just simply a matter of adding things up!

First list out all the forces and add negative (-ive) signs to each of the 'west' forces like this.

20 East + (-27 West) + ? = 10 East

so it's easy to see that 20 + (-27) = -7
So to get to 10 from -7 just do the sum to get 17.
Since 17 is not negative it must be in the direction of East.
So the answer is:
Magnitude = 17 N
Direction = toward the East