Word problem about a semi-elliptical bridge
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Word problem about a semi-elliptical bridge

[From: ] [author: ] [Date: 12-04-09] [Hit: ]
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A bridge is built in the shape of a semi-elliptical arch. The bridge has a span of 60 feet and a maximum height of 20 feet. Choose a suitable rectangular coordinate system and find the height of the arch at a distance of 10 feet from the center.

thanks :)

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x^2 / 30^2 + y^2 / 10^2 = 1

x = 10

10^2 / 30^2 + y^2 / 100 = 1
100/900 + y^2 / 100 = 1
1/9 + y^2 / 100 = 1
y^2 / 100 = 1 - 1/9
y^2 / 100 = 8/9
y^2 = 8 * 100 / 9
y = 2 * 10 * sqrt(2) / 3
y = 20 * sqrt(2) / 3
1
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