In the figure below, the distances between 2 pairs of cities are shown, as well as the angle formed at Ewing, which has a measure of $127^\circ$. Which of the following values is closest to the distance, in miles, from Deerborn to Fergus?

(Note: $\cos{127^\circ}\approx -0.6$; $\sin{127^\circ}\approx 0.8$)

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We can use law of cosines here.

$$c^2=a^2+b^2-2ab\cos{C}$$

Treat angle $C$ as Ewing. The side opposite, which we are to find, is $c$.

$$c^2=80^2+120^2-2(80)(120)\cos{127^\circ}$$ $$c^2 = 32{,}320$$ $$c\approx \boxed{180}$$