Question

A jogger runs 5.0 km on a straight trail at an angle of 60° south of west. What is the southern component of the run rounded to the nearest tenth of a kilometer?

Answer 1

Without rounding off, the answer is -4.33. Since, the southern component of the run of the jogger should be rounded to the nearest tenth of a kilometer, then the answer is -4.3. The answer is negative because it is going south. 

Answer 2

The southern component of the jogger's path is given by:

$S_y = S \sin \theta$

where

$S=5.0 km$ is the total distance of the jogger's run

$\theta=60^{\circ}$ is the angle with respect to the horizontal direction

Substituting numbers into the equation, we find

$S_y=(5.0 km)\sin (60^{\circ})=4.33 km$

and the direction is south.