Solution 5.3a

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From the figure the three known forces can be calculated using,

\displaystyle \begin{align} \mathbf{F} =F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j} \end{align}

We get

\displaystyle \begin{align} \mathbf{F}1 =131\mathbf{i}+47\textrm{.}9 \mathbf{j} \end{align}

\displaystyle \begin{align} \mathbf{F}2 =150 \mathbf{j} \end{align}

\displaystyle \begin{align} \mathbf{F}3 =161\mathbf{i}-135\mathbf{j} \end{align}