Digital ACT Math Practice Question #1262
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{81 + 144 - 108} = \sqrt{117}$.
Apply the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$. Substitute $a = 9$, $b = 12$, and $C = 60^\circ$: $$c^2 = 9^2 + 12^2 - 2(9)(12)\cos(60^\circ) = 81 + 144 - 2(108)(0.5) = 225 - 108 = 117.$$ Thus, $c = \sqrt{117}\text{ nautical miles...
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