An arched footbridge over a 100-foot river is shaped like half an ellipse. The maximum height of the bridge over the river is 20 feet. Find the height of the bridge over a point in the river exactly 25 feet from the center of the river.

The river is 100 feet wide, so the half-ellipse extends 50 feet from its center to either bank. Its horizontal and vertical semi-axes are 50 and 20 feet, giving the equation x²/50² + y²/20² = 1. At x = 25 feet, y = 20√(1 − 25²/50²) ≈ 17.32 feet, which is choice C, 17.32 ft.

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