Answer
$209^{o}$
Work Step by Step
Use:
Magnitude and orientation, (3-6)
$a=\sqrt{a_{x}^{2}+a_{y}^{2}}$ and $\displaystyle \tan\theta=\frac{a_{y}}{a_{x}}$
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From part (a), $\vec{B}=(-23.3\mathrm{m})\hat{i}+(-12.8\mathrm{m})\hat{j}, $
which points towards quadrant III.
$\displaystyle \tan\theta=\frac{B_{y}}{B_{x}}$
$\theta=\tan^{-1}$($\displaystyle \frac{-12.8}{-23.3}$)= (set calculator to degrees) =$28.9^{\mathrm{o}}$,
which is in quadrant I.
In q.III, $\theta=180^{o} +28.9^{o}=209^{o}$
(3 sig. digits)
