How to solve this catenary equation

[Steve Mckenna]

f(x) = a cosh (x/a)

Determine the value of x when f(x) = 48 and a = 35

[leesajohnson]

The links which are shared here is too useful for solving math problems.

[Baltuilhe]

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!