Answer:
2.5882miles
Step-by-step explanation:
-The cyclists keeps a constant angle between them thus forming a virtual isosceles triangle with equal base angles corresponding to their individual 5 mile distances.
-We apply law of Cosines:
[tex]c^2=a^2+b^2-2ab\ Cos \ c[/tex]
#The isosceles base angles are:
[tex]Base \angle s=0.5\times (180-30)\\\\=75\textdegree[/tex]
The distance between them is thus calculated as:
[tex]x^2=a^2+b^2-2ab\ Cos \ x\\\\=5^2+5^2-2\times 5\times 5 \ Cos \ 30\ textdegree\\\\x=\sqrt{6.6987}\\\\=2.5882\ miles[/tex]
Hence, the distance between them is 2.5882miles
