Answer
4.74 km
Work Step by Step
In this case, we need to find the sum of x and y components of a vector with magnitude equal to 3.40 km and making an angle of $35.0^{\circ}$ with x-axis. Therefore, minimum distance she could travel is
$d= 3.40\,km\times\cos 35^{\circ}+ 3.40\,km\times\sin 35^{\circ}$
$=4.74\,km$
Note:
x-component of $\vec{A}= A\cos\theta$
y-component of $\vec{A}=A\sin\theta$ where $\theta$ is the angle $\vec{A}$ makes with the x-axis.
