Question

Help me...How high is a semi-elliptical arch of height 20ft and span 80 ft. at a distance of 15 ft from the end.

Answer 1

Semi-elliptical. This means we have exactly half an ellipse.
If we drop it on a set of coordinate axes, with the Origin in the middle of the street,
its equation is this:


\(y(x) = b^{2} + \sqrt{1 - \dfrac{x^{2}}{a^{2}}}\)

Why didn't I use the negative sing in front of the radical?

We know this: y(40) = y(-40) = 0

It's a little unclear what else we know. I'm taking it to mean that the height of 20 ft is at 15 ft from the outer edge. This gives:

y(25) = y(-25) - 20

That's enough information.