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