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Home » Total distance: \( 150 + 200 = 350 \text km \) - go-checkin.com

Total distance: \( 150 + 200 = 350 \text km \) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 #### 523.33**Question:** An anthropologist is studying the cultural significance of ritualistic dances that trace out geometric patterns in the sand. Suppose a dance forms a regular pentagon with side length \( s \). If each vertex represents a participant who moves to the center of the pentagon, calculate the total distance traveled by all participants from their initial positions to the center. Use \( s \) for the side length.

📌 To solve this, we first recognize that the center of a regular pentagon is equidistant from all its vertices. The distance from a vertex to the center (the radius \( R \)) of a regular pentagon can be found using the formula:

📌 R = \frac{s}{2 \sin(\pi/5)}

📌 The sine of \( \pi/5 \) is \( \sin(\pi/5) = \sin(36^\circ) \), which is approximately \( 0.5878 \). Thus,

📌 R = \frac{s}{2 \times 0.5878} \approx \frac{s}{1.1756} \approx 0.8507s

📌 Since there are 5 participants, each moving from a vertex to the center, the total distance traveled is:

📌 \times R = 5 \times 0.8507s = 4.2535s

📌 Thus, the total distance traveled by all participants is:

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