Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Explanation :
Since we have shown in the figure below :
a=70 mi.
b=52 mi.
c=x mi.
[tex]\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}[/tex]
So, we use the cosine rule , which states that
[tex]c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03[/tex]
So, c = x= 106.03 mi.
Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
