Triangle Square: How Does the Largest Equilateral Triangle Fit Inside a Square?

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The largest equilateral triangle that fits inside a square is oriented at 15 degrees above the horizontal, with one vertex positioned at a corner of the square. This specific orientation maximizes the area of the triangle while ensuring it remains entirely within the boundaries of the square. The triangle's other vertices touch the square's sides, demonstrating an optimal geometric arrangement. Understanding this configuration is crucial for solving related geometric problems. The discussion highlights the importance of orientation in maximizing space within geometric shapes.
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What is the orientation of the largest equilateral triangle contained within a square?
 
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