ACT Math Practice Question #1260 (Medium (32)) | Test Citadel
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ACT Math Difficulty: Medium (32)

Digital ACT Math Practice Question #1260

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In a triangular municipal park, surveyors map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $7\text{ meters}$, the distance from $B$ to $C$ is $10\text{ meters}$, and the measure of angle $C$ is $60^\circ$. What is the direct straight-line distance, in meters, from marker $A$ to marker $B$?
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{49 + 100 - 70} = \sqrt{79}$.

Masterclass Solution & Distractor Trap Analysis

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, $c = \sqrt{79}\text{ meters}$....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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