The Gateway Arch in St Louis Missouri was constructed using

The Gateway Arch in St. Louis, Missouri was constructed using the hyperbolic cosine function. The equation used for construction was

y=693.8597 - 68.7672cosh0.0100333x, -299.2239 <= x <= 299.2239

where x and y are measured in feet. Cross sections of ther arch are equilateral triangles, and (x,y) traces a path of the centers of mass of the cross section triangles. For each value of x, the area of the cross section is

A= 125.1406cosh0.0100333x

(a) How high above the ground is the center of the highest triangle?(At ground level, y = 0.)

(b) What is the height of the arch? (Hint: For an equilateral triangle, A = sqrt(3)c^2, where c is one-half the base of the triangle, and the center of mass of the triangle is located at two-thirds the height of the triangle.)

(c) How wide is the arch at ground level?
  

Solution