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tekilochka [14]
3 years ago
14

Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other

52 mi. before they each drop their anchors. What is the distance between the ships to the nearest mile?

Mathematics
1 answer:
kondaur [170]3 years ago
8 0

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.

\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}

So, we use the cosine rule , which states that

 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

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.


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