ACT Math Practice Question #1264 (Medium (32)) | Test Citadel
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ACT Math Difficulty: Medium (32)

Digital ACT Math Practice Question #1264

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In a flight path between two regional waypoints, air traffic controllers map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $8\text{ miles}$, the distance from $B$ to $C$ is $15\text{ miles}$, and the measure of angle $C$ is $60^\circ$. What is the direct straight-line distance, in miles, from marker $A$ to marker $B$?
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{64 + 225 - 120} = \sqrt{169}$.

Masterclass Solution & Distractor Trap Analysis

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, $c = \sqrt{169}\text{ miles}$....

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

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