An arch is of the form of a semi-ellipse, with its major axis as the span of the arch. If the span is 80 m and the height is 30m, find the height of the arch at a point 15 m from the minor axis.

Expert Answers

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The equation of the arch curve is:

`x^2/(40)^2+y^2/(30)^2=1`

`x^2/1600+y^2/900=1`

Solve for y.

`y^2/900=1-x^2/1600`

`y=30sqrt(1-x^2/1600)`

Substitute 15 for x.

`y=(30)sqrt(1-15^2/1600)`

`y=(30)(sqrt(0.8593))=27.8m`

Thus the height of the arc at 15m from the minor axis is 27.8m.

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