Chapter 6.9, Problem 73ES

The design of the Gateway Arch in St. Louis, Missouri, by architect Eero Saarinan was implemented using equations provided by Dr. Hannskarl Badel. The equation used for

the centerline of the arch was

$y=693.8597-68.7672\cosh \left(0.0100333x\right)\text{ ft}$

for $x$ between $-299.2239$ and $299.2239$ .

(a) Use a graphing utility to graph the centerline of the arch.

(b) Find the length of the centerline to four decimal places.

(c) For what values of $x$ is the height of the arch $100\text{ ft}$ ? Round your answers to four decimal places.

(d) Approximate, to the nearest degree, the acute angle that the tangent line to the centerline makes with the ground at the ends of the arch.