Answer: The component is 2km
Explanation:
Jim walked 4km on a straight path, and the angle is 30° south of the east (so, looking at the east direction, he walked with 30° angle in direction to the south)
So in the rectangle triangle, the east segment is the adjacent side, and the south segment is the opposite side. And 4km is the length of the hypotenuse.
Here you can remember the rule:
soh-cah-toa
this means Sin(a)=Opposite side/hypotenuse
cos(a) = adjacent side/hypotenuse
tan(a) = opposite side/adjacent side
where a is the angle, in this case, a= 30°
Them if we want to find the southern component, we must do:
S = 4km*sin(30°) = 2km
Them the component in the southern direction is 2km