Question

The ""Hatch Shell"" in Boston has the arch with semi-elliptical form with a horizontal major axis. The base of the arch is 110-foot long and the highest part of the arch is 40 feet above the scene. Find the height of the arch of the ""Hatch Shell"" 33 feet away from the midpoint of the base of the arch.

Answer 1

Answer:32 ft

Explanation:

Given

Hatch shell is in the form of semi-Elliptical Ellipse

whose base =110 ft

highest part of Arch is 40 ft

Equation of Ellipse

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

here 2a=110

a=55, b=40

For x=33 feet away from midpoint i.e. origin of ellipse y =

$\frac{33^2}{55^2}+\frac{y^2}{40^2}=1$

$\frac{y^2}{40^2}=1-0.36=0.64$

$\frac{y}{40}=0.8$

$y=0.8\times 40=32 ft$