Digital ACT Math Practice Question #1261
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{25 + 64 - 40} = \sqrt{49}$.
Apply the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$. Substitute $a = 5$, $b = 8$, and $C = 60^\circ$: $$c^2 = 5^2 + 8^2 - 2(5)(8)\cos(60^\circ) = 25 + 64 - 2(40)(0.5) = 89 - 40 = 49.$$ Thus, $c = \sqrt{49}\text{ kilometers}$....
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