Answer:
Explanation: Ok, first caracterize the two vectors that we know.
A = ax + ay = (12*cos(40°)*i + 12*sin(40°)*j) m
now, see that C is angled 20° from -x, -x is angled 180° counterclockwise from +x, so C is angled 200° counterclockwise from +x
C = cx + cy = (15*cos(200°)*i + 15*sin(200°)*j) m
where i and j refers to the versors associated to te x axis and the y axis respectively.
in a sum of vectors, we must decompose in components, so: ax + bx = cx and ay + by = cy. From this two equations we can obtain B.
bx= (15*cos(200°) - 12*cos(40°)) m = -23.288 m
by = (15*sin(200°) - 12*sin(40°)) m = -12.843 m
Now with te value of both components of B, we proceed to see his magnitude an angle relative to +x.
Lets call a to the angle between -x and B, from trigonometry we know that tg(a) = by/bx, that means a = arctg(12.843/23.288) = 28.8°
So the total angle will be 180° + 28.8° = 208.8°.
For the magnitude of B, lets call it B', we can use the angle that we just obtained.
bx = B'*cos(208.8°) so B' = (-23.288 m)/cos(208.8°) = 26.58 m.
So the magnitude of B is 26.58 m.
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