Answer:
-75.35°
Explanation:
Let C be the sum of the two vectors A and B. Hence, we can write the following
[tex]A_{x} +B_{x} =C_{x} ......(1)\\A_{y} +B_{y} =C_{y} ......(2)[/tex]
but since the vector C is in the -y direction, [tex]C_{x}[/tex] = 0 and [tex]C_{y}[/tex] = —12 m.
Thus
[tex]B_{x} =-A_{x} =-[-Acos(180-127)]=(8)*cos(53)\\B_{x} =4.81m[/tex]
similarly, we can determine [tex]B_{y}[/tex] by rearranging equation (1)
[tex]B_{y} =C_{y} -A_{y} =-12m-[(8)*sin(53)\\B_{y} =-18.4m[/tex]
so the magnitude of B is
[tex]B=\sqrt{B_{x}^2+B_{y}^2 } \\B=19m[/tex]
Finally, the direction of B can be calculated as follows
Ф=[tex]tan^{-1} (\frac{B_{y} }{B_{x} } )\\=-75.35[/tex]
hence the vector B makes an angle of 75.35 clockwise with + x axis
