An explorer is caught in a whiteout $($in which the snowfall is so thick that the ground cannot be distinguished from the sky$)$ while returning to base camp. He was supposed to travel due north for $5\mathrm{.}1km,$ but when the snow clears, he discovers that he actually traveled $8\mathrm{.}5km$ at $52$ north of due east. $($a$)$ How far and $($b$)$ in what direction $($south of due west$)$ must he now travel to reach base camp?

$($a$)$ Number

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$($b$)$ Number

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