Good morning!
Just to help another people who could have searched for 'catenary', like me
[tex]f(x)=a\cdot\cosh\left(\dfrac{x}{a}\right)[/tex]
Given data:
[tex]\begin{cases}f(x)=48\\a=35\end{cases}[/tex]
Calculating:
[tex]48=35\cdot\cosh\left(\dfrac{x}{35}\right)\\
\dfrac{48}{35}=\cosh\left(\dfrac{x}{35}\right)\\
\dfrac{x}{35}=\cosh^{-1}\left(\dfrac{48}{35}\right)\\
x=35\cdot\cosh^{-1}\left(\dfrac{48}{35}\right)\\
\boxed{x\approx 29,3029}[/tex]
I Hope to have helped!