# How to solve this catenary equation

### How to solve this catenary equation

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

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

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### Re: How to solve this catenary equation

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

leesajohnson

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### Re: How to solve this catenary equation

Good morning!

Just to help another people who could have searched for 'catenary', like me

$$f(x)=a\cdot\cosh\left(\dfrac{x}{a}\right)$$

Given data:
$$\begin{cases}f(x)=48\\a=35\end{cases}$$

Calculating:
$$48=35\cdot\cosh\left(\dfrac{x}{35}\right)\\ \dfrac{48}{35}=\cosh\left(\dfrac{x}{35}\right)\\ \dfrac{x}{35}=\cosh^{-1}\left(\dfrac{48}{35}\right)\\ x=35\cdot\cosh^{-1}\left(\dfrac{48}{35}\right)\\ \boxed{x\approx 29,3029}$$

I Hope to have helped!

Baltuilhe

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