An arch of a bridge is built in the shape of half an ellipse. It has a span of 120 feet. The height of the arch 20 feet from the center is 18 feet. Find the height at the center.
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Let the center of the ellipse coincide with the origin of cartesian
xy-coordinate axes.
Then, the ellipse equation is: x²/a² + y²/b² = 1,
where, a = 60', x = 20', y = 18'.
Solve for b:
20²/60² + 18²/b² = 1, b = √[18²/0.888] = 19.1'
xy-coordinate axes.
Then, the ellipse equation is: x²/a² + y²/b² = 1,
where, a = 60', x = 20', y = 18'.
Solve for b:
20²/60² + 18²/b² = 1, b = √[18²/0.888] = 19.1'