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Answer:
One must drive [tex]$41 \cdot 8\,miles$[/tex] north and [tex]$68 \cdot 24\,miles$[/tex] south, in order to travel from Atlanta to Macon.
Explanation:
• The distance of an object can be defined as the complete path travelled by an object.
• To find the distance, find its north component.
• For reference see the below graph:
[tex]$\[\begin{align}& D_{south} = 80\sin \left( {58 \cdot {5^ \circ }} \right) \\& D_{north} = 80\cos \left( {58 \cdot {5^ \circ }} \right) \\\end{align}\]$Since, $\sin \left( {58 \cdot {5^ \circ }} \right) = \cdot 853$ and $\cos \left( {58 \cdot {5^ \circ }} \right) = \cdot 5224$: therefore,$\[\begin{align} D_{south} &= 80 \times \left( { \cdot {{853}^ \circ }} \right) \\ \Rightarrow {D_{south}} &= 68 \cdot 24\,miles \\ \end{align}\]$[/tex]
And
[tex]$\[\begin{align} D_{north}& = 80 \times \cdot 5224 \\ \Rightarrow D_{north}& = 41 \cdot 8\,miles \\ \end{align}\]$[/tex]
• Hence, one must drive [tex]$41 \cdot 8\,miles$[/tex] north and [tex]$68 \cdot 24\,miles$[/tex] south, in order to travel from Atlanta to Macon.
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