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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Pregunta: Un educador matemático diseña un acertijo geométrico: en un triángulo rectángulo, si $ \tan \theta = \frac{5}{12} $, ¿cuál es $ \sin 2\theta $?

📌 A) $ \frac{120}{169} $

📌 B) $ \frac{120}{13} $

📌 C) $ \frac{24}{169} $

📌 D) $ \frac{5}{13} $

📌 E) $ \frac{60}{169} $

📌 Respuesta correcta: A) $ \frac{120}{169} $

📌 Because $ \tan \theta = \frac{5}{12} \Rightarrow $ opposite = 5, adjacent = 12, hyp = 13. Then $ \sin \theta = \frac{5}{13} $, $ \cos \theta = \frac{12}{13} $, so $ \sin 2\theta = 2 \sin\theta \cos\theta = 2 \cdot \frac{5}{13} \cdot \frac{12}{13} = \frac{120}{169} $.

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