Answer
$127\space km,\space \theta=74^{\circ}$
Work Step by Step
Please see the attached image first.
Here we use the component method to find the magnitude and direction of the resultant vector.
Let's take the resultant vector equal to $R.$ Then we can write.
$\vec R=\vec A+\vec B$
x component of the resultant vector $R_{x}=A_{x}+B_{x}$ ; Let's plug known values into this equation.
$R_{x}=244\space km\times cos30^{\circ}+(-175\space km)=36\space km$
y component of the resultant vector $R_{y}=A_{y}+B_{y}$ ; Let's plug known values into this equation.
$R_{y}=244\space km\times sin30^{\circ}=122\space km$
By using the Pythagorean theorem, we can get.
$R=\sqrt {R_{x}^{2}+R_{y}^{2}}=\sqrt {(36\space km)^{2}+(122\space km)^{2}}=127\space km$
By using trigonometry, we can get.
$tan\theta=\frac{R_{y}}{R_{x}}=\frac{122\space km}{36\space km}=>\theta=tan^{-1}(3.4)=74^{\circ}$
