Question

The Golden Gate bridge in San Francisco, CA is a catenary suspension bridge, which is very similar in appearance to a parabola. The main span cables are suspended between two towers that are 4200 ft. apart and 500 ft. above the roadway. The cable extends 10' above the roadway midway between the two towers.

a. Write an equation that models the shape of the cable.

b. How far from the roadway is the cable 720 ft. from the bridge's center?

Please help me get to the right direction because I don't even know where to begin.

Answer 1

When I googled `catenary curve` it gave me this equation:\[\Large\rm y=a \cosh\left(\frac{x}{a}\right)\]But I can't seem to make that work....
Let's try using this instead:\[\Large\rm y=a \cosh\left(\frac{x}{b}\right)\]
Ok let's start by drawing out the diagram.