the tunnel in a mountain has semi-elliptical arc

Question

The tunnel in a mountain has semi-elliptical arch. If it has a major axis of 50 feet and a height at the center of 10 feet, how high is the arch from the ground at 17 feet from the center?

Answer 1

Use the equation for a semi-ellipse centered on the origin:

f(x) = ^b/_a √(a² - x²)

In this case, b = 10 and a = 25, so f(x) = ¹⁰/₂₅ √(25² - x²)

Calculate f(17) = 7.33