Question

Jin walked 4 km on a straight path to get to the sandwich shop. He traveled 30° south of east.

Answer 1

Answer: -2 km

Explanation:

If we imagine Jin's movement to be the hypothenuse of a right triangle, then the southern component of Jin's movement corresponds to the side of the triangle opposite to the angle of 30 degrees. Therefore, the magnitude of this southern component is given by

However, the angle of 30 degrees is south of east: this means that the direction of this southern component is south, and since we generally take north as positive direction, we must add a negative sign, so the correct answer is

-2 km

Answer 2

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