Chapter 6.5, Problem 38E

Gateway Arch The shape of the Gateway Arch in St. Louis (with a height and a base length of 630 ft) is modeled by the function y = −630 cosh (x/239.2) + 1260, where |x| ≤ 315, and x and y are measured in feet (see figure). The function cosh x is the hyperbolic cosine, defined by $\cosh x=\frac{e^x+e^{-x}}{2}$ (see Section 6.10 for more on hyperbolic functions). Estimate the length of the Gateway Arch.