Digital ACT Math Practice Question #1264
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{64 + 225 - 120} = \sqrt{169}$.
Apply the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$. Substitute $a = 8$, $b = 15$, and $C = 60^\circ$: $$c^2 = 8^2 + 15^2 - 2(8)(15)\cos(60^\circ) = 64 + 225 - 2(120)(0.5) = 289 - 120 = 169.$$ Thus, $c = \sqrt{169}\text{ miles}$....
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