Answer
The force required to pull the box is 30.9 pounds.
Work Step by Step
${{\mathbf{F}}_{1}}=-100\mathbf{j}$
Find the length of BC as below:
$\begin{align}
& {{\mathbf{F}}_{\mathbf{2}}}=95\cos 288{}^\circ \mathbf{i}+95\sin 288{}^\circ \mathbf{j} \\
& =29.41\mathbf{i}-90.4\mathbf{j}
\end{align}$
The resulting vector will be obtained as below:
$\begin{align}
& \mathbf{F}={{\mathbf{F}}_{1}}-{{\mathbf{F}}_{\mathbf{2}}} \\
& =\left( -100\mathbf{j} \right)-\left( 29.4\mathbf{i}-90.4\mathbf{j} \right) \\
& =-29.4\mathbf{i}-9.6\mathbf{j}
\end{align}$
So, the magnitude of force vector is given by
$\begin{align}
& \left| \left| \mathbf{F} \right| \right|=\sqrt{{{\left( -29.4 \right)}^{2}}+{{\left( -9.6 \right)}^{2}}} \\
& \approx 30.9
\end{align}$
