SOLUTION: An arch is in the form of a semiellipse. It is 48 ft wide at the base and has a height of 20ft. How wide is the arch at a height of 10 ft above the base?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: An arch is in the form of a semiellipse. It is 48 ft wide at the base and has a height of 20ft. How wide is the arch at a height of 10 ft above the base?      Log On


   



Question 1184728: An arch is in the form of a semiellipse. It is 48 ft wide at the base and has a
height of 20ft. How wide is the arch at a height of 10 ft above the base?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An arch is in the form of a semiellipse. It is 48 ft wide at the base and has a
height of 20ft. How wide is the arch at a height of 10 ft above the base?
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Equation of the ellipse is (center at the Origin)
x%5E2%2F576+%2B+y%5E2%2F400+=+1
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At y = 10:
x%5E2%2F576+%2B+100%2F400+=+1
x%5E2%2F576+=+3%2F4
x%5E2+=+432
x = ~20.78 (each side of the Origin)
Width = ~ 41.57 feet