A bridge is built in the shape of a semielliptical arch. It has a span of 112 feet. The height of the arch 26 feet from the center is to be 12 feet. Find the height of the arch at its center.

Question

Mathematics

Blake Warren

23 July, 13:22

A bridge is built in the shape of a semielliptical arch. It has a span of 112 feet. The height of the arch 26 feet from the center is to be 12 feet. Find the height of the arch at its center.

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Tatum · Answer 1

Solve this using standard form of ellipse equation: (x-h) ^2 / a^2 + (y-k) ^2 / b^2 = 1.

Put the center of the ellipse at (0,0), then h=k=0, so that simplifies things. If the span is 112 feet, then the semi-major axis in the x direction is 56, that would be 'a' I think you have to use the given information to solve for 'b.'

Getting 13.5488, so 13.5 or 13.55 feet seems fine as a rounded answer.