SOLUTION: an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a he

Question 751050: an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a height of 10ft from the base?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a height of 10ft from the base?
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Equation of ellipse with horizontal major axis and center at (0,0)

For given problem:
a=25
a^2=625
b=20
b^2=400
Equation:

..
find height 10 ft from center of base: (10,y)
100/625+y^2/400=1
y^2/400=1-100/625=0.84
y^2=0.84*400=336
y=�√336=�18.34
height at a distance of 10ft from the centre of the base≈18.34 ft
..
find width at height 10 ft from base (x,10)
x^2/625+100/400=1
x^2/625=1-100/400=0.75
x^2=0.75*625=468.75
x=�√468.75=�21.65
width at height 10 ft from base=2*21.65≈43.3 ft
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