Answer:
The two towns are 62.57km apart.
Explanation:
A diagram representing the problem is redrawn and attached below:
From trigonometric ratios:
[tex]\begin{gathered} \tan 55\degree=\frac{53}{OA} \\ OA\times\tan 55\degree=53 \\ OA=\frac{53}{\tan 55\degree} \\ OA=37.11\operatorname{km} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \tan 28\degree=\frac{53}{OB} \\ OB\times\tan 28\degree=53 \\ OB=\frac{53}{\tan 28\degree} \\ OB=99.68\operatorname{km} \end{gathered}[/tex]Therefore, the distance between the two towns is:
[tex]\begin{gathered} AB=OB-OA \\ =99.68-37.11 \\ =62.57\operatorname{km} \end{gathered}[/tex]The two towns are 62.57km apart.
