ACT Math Practice Question #1200 (Medium (32)) | Test Citadel
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ACT Math Difficulty: Medium (32)

Digital ACT Math Practice Question #1200

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

In $\triangle ABC$, the length of side $a$ is $8$ cm, the length of side $b$ is $11$ cm, and the measure of angle $C$ between them is $60^\circ$. What is the exact length, in centimeters, of side $c$?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Recall $\cos(60^\circ) = 1/2$. The $2ab\cos(C)$ term simplifies directly to $ab = 8 \times 11 = 88$. Compute $64 + 121 - 88 = 97$ in under 15 seconds.

Masterclass Solution & Distractor Trap Analysis

Apply the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$. Substituting the given values: $c^2 = 8^2 + 11^2 - 2(8)(11)\cos(60^\circ) = 64 + 121 - 176(0.5) = 185 - 88 = 97$. Therefore, $c = \sqrt{97}$....

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

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