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## Homework Statement

Given F1= 36N[25degrees N of E] and F2= 42N [15 degrees E of S], determine the force F3 that must be added to the sum of F1+F2 to produce a net force of zero.

## Homework Equations

Sine law, a/sina= b/sinb

Cosine law: c^2= a^2 + b^2- 2(a)(b) Cos(theta)

## The Attempt at a Solution

I first went about the question by drawing a vector diagram of all the two know forces, and then I broke down each force into horizontal and vertical components.

For F1:

F1y= 36N sin25

F1y= 15.2N

F1x= 36NCos25

F1x= 32.6N

For F2:

F2y= 42NCos15

F2y= 40.5N

F2x= 42NSin15

F2x= 10.8N

Then I added all of the x and y values:

ƩFx= 32.6N +10.8N

ƩFx= 43.4N

ƩFy= 40.5N +15.2N

ƩFy=55.7N

I then went on to find the resultant vector:

F=√43.4N^2 + 55.7N^2

F=70.6N

From this point on I have no idea where to go.