Solution 5.5a

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\displaystyle \begin{align} & \mathbf{F}= F\cos \alpha \mathbf{i}+F\sin \alpha \mathbf{j} =\left( 5000\times \cos {{25}^{\circ }} \right)\mathbf{i}+\left( 5000\times \sin {{25}^{\circ }} \right)\mathbf{j} \\ & \\ & =\left( 5000\times 0\textrm{.}906 \right)\mathbf{i}+\left( 5000\times 0\textrm{.}422 \right)\mathbf{j} \\ & \\ & =4530\mathbf{i}+2113\mathbf{j}\ \text{N} \\ \end{align}