Arace car driver on the flats first heads north for 6.71 km, then makes a sharp turn and heads southwest for 1.33 km, then makes another turn and heads east for 3.67 km. how far is she from where she started?

D=7.385km

Explanation:

First we calculate how much it moves vertically (north and south), we will call this distance Y,.

taking into account that the car moves to the southwest and that it has a slope of 45 degrees, we can say that the component that moved south can be subtracted from the distance that moved north.

Y=6.71-1.33sen45=5.77km

then the distance that moves in the east we will call it X

we can add the component of the distance that moves to the southwest with the distance that moves to the east

X=3.67+1.33cos45=4.61Km

then we use the distance equation

D=7.385km

nah.   i'm just sleepy.