SOLUTION: A 28-newton force acting at 42° and a 65-newton force acting at 24° act concurrently on an object. What is the magnitude and direction of a third force that produces equilibrium on

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Question 1036853: A 28-newton force acting at 42° and a 65-newton force acting at 24° act concurrently on an object. What is the magnitude and direction of a third force that produces equilibrium on the object?
Magnitude = 85.6 N; Direction = 210°
Magnitude = 92 N; Direction = 209°
Magnitude = 92 N; Direction = 29°
Magnitude = 92 N; Direction = 241°
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So by equilibrium, the sum of the forces in the x and y directions would equal zero.
F%5B1x%5D=28%2Acos%2842%29=20.81
F%5B1y%5D=28%2Asin%2842%29=18.74
F%5B2x%5D=65%2Acos%2824%29=59.38
F%5B2y%5D=65%2Asin%2824%29=26.44
So then,
F%5B1x%5D%2BF%5B2x%5D%2BF%5B3x%5D=0
20.81%2B59.38%2BF%5B3x%5D=0
F%5B3x%5D=-80.19
and
F%5B1y%5D%2BF%5B2y%5D%2BF%5B3y%5D=0
18.74%2B26.44%2BF%5B3y%5D=0
F%5B3y%5D=-45.18
So then,
abs%28F%5B3%5D%29=sqrt%28F%5B3x%5D%5E2%2BF%5B3y%5D%5E2%29
abs%28F%5B3%5D%29=sqrt%2880.19%5E2%2B45.18%5E2%29
abs%28F%5B3%5D%29=sqrt%288471.67%29
abs%28F%5B3%5D%29=94.02
and
tan%28theta%29=F%5B3y%5D%2FF%5B3x%5D
tan%28theta%29=45.18%2F80.19
tan%28theta%29=0.5634
Since both are negative, theta is in Quadrant 3.
theta=209.4