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An entrepreneur is designing a solar panel installation on a triangular plot of land with side lengths of 13, 14, and 15 meters. To optimize sunlight exposure, they need to find the length of the shortest altitude of the triangle.
A cartographer is mapping a terrain where a right triangle-shaped field has a hypotenuse of 10 meters and an inscribed circle radius of 2 meters. Calculate the ratio of the area of the circle to the area of the triangle.