Question 1206226
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<table border = "1" cellpadding = "5"><tr><td>Vector</td><td>Magnitude</td><td>Angle</td></tr><tr><td>A</td><td>r</td><td>75 </td></tr><tr><td>B</td><td>s</td><td>180 </td></tr><tr><td>C</td><td>185</td><td>270 </td></tr></table>

Each vector can be written in component form: (x,y) = (m*cos(theta), m*sin(theta))
where,
m = magnitude
theta = angle


vector A:  (r*cos(75), r*sin(75))
vector B:  (s*cos(180), s*sin(180)) = (-s, 0)
vector C:  (185*cos(270), 185*sin(270)) = (0, -185)


In other words,
vector A:  (r*cos(75), r*sin(75))
vector B:  (-s, 0)
vector C:  (0, -185)


Add the vectors by adding the corresponding components.
If (x,y) and (v,w) are two vectors, then they sum to (x+v, y+w).
This can be extended to 3 vectors or more.


A+B+C = (r*cos(75) - s, r*sin(75) - 185)


This resultant vector is stated to be the zero vector (0,0).


Set each component equal to zero so we form this system of equations.
r*cos(75) - s = 0
r*sin(75) - 185 = 0


Solving the second equation for variable r gets us: 
r = 185/sin(75) = 191.526093 approximately.
Make sure that your calculator is in degrees mode.


Then,
r*cos(75) - s = 0
s = r*cos(75)
s = 191.526093*cos(75)
s = 49.570601 approximately


In summary we found these approximations,
r = 191.526093
s = 49.570601
which represent the magnitudes of vectors A and B respectively.
Round these decimal values however needed.
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