A pilot flies her route in two straight$-$line segments. The displacement vector $\backslash (\backslash$mathbf$\{$A$\}\backslash )$ for the first segment has a magnitude of $259$ km and a direction $\backslash (30\mathrm{.}0^\{\backslash$circ$\}\backslash )$ north of east. The displacement vector B for the second segment has a magnitude of $165$ km and a direction due west. The resultant displacement vector is $\backslash (\backslash$mathbf$\{$R$\}=\backslash$mathbf$\{$A$\}+\backslash$mathbf$\{$B$\}\backslash )$ and makes an angle $\backslash (\backslash$theta $\backslash )$ with the direction due east. Using the component method, find $(\backslash (\backslash$mathbf$\{$a$\}\backslash ))$ the magnitude of $\backslash (\backslash$mathbf$\{$R$\}\backslash )$ and $($b$)$ the directional angle $\backslash (\backslash$theta $\backslash ).$

$($a$)\backslash ($ R$=\backslash )$ Number

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$($b$)\backslash (\backslash$theta$=\backslash )$ Number

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