ACT Math Practice Question #1263 (Medium (32)) | Test Citadel
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ACT Math Difficulty: Medium (32)

Digital ACT Math Practice Question #1263

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In a triangular suspension bridge truss, structural engineers map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $6\text{ feet}$, the distance from $B$ to $C$ is $10\text{ feet}$, and the measure of angle $C$ is $60^\circ$. What is the direct straight-line distance, in feet, from marker $A$ to marker $B$?
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Because $\cos(60^\circ) = 1/2$, the formula simplifies immediately to $c = \sqrt{a^2 + b^2 - ab} = \sqrt{36 + 100 - 60} = \sqrt{76}$.

Masterclass Solution & Distractor Trap Analysis

Apply the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$. Substitute $a = 6$, $b = 10$, and $C = 60^\circ$: $$c^2 = 6^2 + 10^2 - 2(6)(10)\cos(60^\circ) = 36 + 100 - 2(60)(0.5) = 136 - 60 = 76.$$ Thus, $c = \sqrt{76}\text{ feet}$....

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

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