Calculate the $x$ and $y$ components of $\stackrel{\rightharpoonup }{A}$ using the formulas $A_x=❘A❘\cos \left(\mathrm{\angle A}\right)$ and $A_y=❘A❘\sin \left(\mathrm{\angle A}\right)$.

$\stackrel{\rightharpoonup }{A}=⟨4\cos \left(54°\right),4\sin \left(54°\right)⟩$

Calculate the $x$ and $y$ components of $\stackrel{\rightharpoonup }{B}$ using the formulas $B_x=❘B❘\cos \left(\mathrm{\angle B}\right)$ and $B_y=❘B❘\sin \left(\mathrm{\angle B}\right)$.

$\stackrel{\rightharpoonup }{B}=⟨3\cos \left(310°\right),3\sin \left(310°\right)⟩$

Calculate the $x$ and $y$ components of the sum of vectors $A$ and $B$.

If $\stackrel{\rightharpoonup }{S}=\stackrel{\rightharpoonup }{A}+\stackrel{\rightharpoonup }{B}$, $S_x=A_x+B_x$ and $S_y=A_y+B_y$.

Vector sum:

$\stackrel{\rightharpoonup }{A}+\stackrel{\rightharpoonup }{B}=⟨4\cos \left(54°\right),4\sin \left(54°\right)⟩+⟨3\cos \left(310°\right),3\sin \left(310°\right)⟩$

$\stackrel{\rightharpoonup }{A}+\stackrel{\rightharpoonup }{B}=⟨4\cos \left(54°\right)+3\cos \left(310°\right),4\sin \left(54°\right)+3\sin \left(310°\right)⟩$

Calculate the magnitude of the sum of vectors $A$ and $B$ using the formula $❘S❘=\sqrt{S_x^2+S_y^2}$.

The magnitude of $\stackrel{\rightharpoonup }{A}+\stackrel{\rightharpoonup }{B}$ is $\sqrt{{\left(4\cos \left(54°\right)+3\cos \left(310°\right)\right)}^2+{\left(4\sin \left(54°\right)+3\sin \left(310°\right)\right)}^2}=4.38$.

Hence, the magnitude of $\stackrel{\rightharpoonup }{A}+\stackrel{\rightharpoonup }{B}$ is $4.38$.