Answer
$$\mathbf{u}+\mathbf{v}=\left(5,\sqrt{3}\right)$$
Work Step by Step
$\|\mathbf{u}\|=4\hspace{5mm}\theta_u=0^\circ$
$\|\mathbf{v}\|=2\hspace{5mm}\theta_v=60^\circ$
$u_x=\|\mathbf{u}\|\cos{\theta_u}=4\cos{0}=4$
$u_y=\|\mathbf{u}\|\sin{\theta_u}=4\sin{0}=0$
$v_x=\|\mathbf{v}\|\cos{\theta_v}=2\cos{60}=2\frac{1}{2}=1$
$v_y=\|\mathbf{v}\|\sin{\theta_v}=2\sin{60}=2\frac{\sqrt{3}}{2}=\sqrt{3}$
Therefore,
$\mathbf{u}+\mathbf{v}=\left(4+1,0+\sqrt{3}\right)$
$$\mathbf{u}+\mathbf{v}=\left(5,\sqrt{3}\right)$$
