Answer
$(1.28m)\hat{\mathrm{i}}+(6.60m)\hat{\mathrm{j}}$
Work Step by Step
Using (3-5) for vector components,
$ a_{x}=a\cos\theta$ and $ a_{y}=a\sin\theta$.
Set your calculator to radians,
$\vec{E}=3.73\hat{\mathrm{i}}+4.70\hat{\mathrm{j}}$
$\vec{G}=1.45\hat{\mathrm{i}}+3.73\hat{\mathrm{j}}$
Set your calculator to degrees.
$\vec{F}=1.29\hat{\mathrm{i}}-4.83\hat{\mathrm{j}}$
$\vec{H}=-5.20\hat{\mathrm{i}}+3.00\hat{\mathrm{j}}$
The resultant sum of the vectors is obtained by using (3-10 to 3-12):
$\vec{E}+\vec{F}+\vec{G}+\vec{H}=[(3.73+1.45+1.29-5.20)m]\hat{i}$
$+[(4.70+3.73-4.83+3.00)m]\hat{j}$
$=(1.28m)\hat{\mathrm{i}}+(6.60m)\hat{\mathrm{j}}$.
