Question 976252
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a one-way road passes under an overpass in the shape of half and ellipse, 30ft high at the center and 20ft wide. 
Assuming a truck is 12ft wide, what is the tallest truck that can pass under the overpass?
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        Calculations in the post by @lwsshak3 are incorrect, leading to wrong answer.

        I came to provide a correct solution.



Ellipse has a vertical major axis
Its basic form of equation:
x^2/b^2+y^2/a^2=1
For given problem:
a=30
b=10
equation: x^2/10^2+y^2/30^2=1
=x^2/100+y^2/900=1
coordinates of point at which a 12 ft wide truck would reach the overpass=(6,y)
plug in x-coordinate and solve for y
y^2/900=1-x^2/100=1-36/100=64/100    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<<<---===  this is the point where @lwsshak3 made his mistake
y^2=9*64=576
y=√576 = 24


what is the tallest truck that can pass? < 24 ft



More accurately, the conception "tallest truck" does not work in this problem, 
so the question is posed incorrectly in the post.


A correct question should ask about the set of possible heights.
Then the answer  " h < 24 ft " is correct and accurate.



Solved correctly.