Digital ACT Math Practice Question #1260
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{49 + 100 - 70} = \sqrt{79}$.
Apply the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$. Substitute $a = 7$, $b = 10$, and $C = 60^\circ$: $$c^2 = 7^2 + 10^2 - 2(7)(10)\cos(60^\circ) = 49 + 100 - 2(70)(0.5) = 149 - 70 = 79.$$ Thus, $c = \sqrt{79}\text{ meters}$....
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