The arch of a bridge is in the form of an arc of a circle. If the span of the bridge is 40 m and height in the middle is 8 m, then what is the radius of curvature of the bridge?

Explanation

Let the radius be R. The half-span is 20 m and forms a right triangle with the center and distance (R-8) to the chord. By Pythagoras: (R-8)^2 + 20^2 = R^2 \implies 16R = 464 \implies R = 29 m.

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