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In order to find the length of the trail, we need to use the distance formula. Thus, we need to form two coordinates. When Dave and Caroline start, they have walked $0$ feet in horizontal direction and they are $1533$ feet up in vertical direction.
$Start:(0,1533)$
When they finished the track they will be $35421$ feet away from the start in horizontal direction and $5641$ above the ocean.
$End:(35421,5641)$
We will now substitute the points into the distance formula.
The length of the trail is about $1271522905 $ feet. Note that we keep our answer in exact form to avoid having to round our answer twice. Since there are $5280$ feet in one mile, to convert this distance into miles we have to divide it by $5280.$
$52801271522905 ≈6.75 $
The length of the trail is about $6.75$ miles.

$d=(x_{2}−x_{1})_{2}+(y_{2}−y_{1})_{2} $

$d=(35421−0)_{2}+(5641−1533)_{2} $

$d=1271522905 $