# Angle between catenary and line

1. Apr 27, 2008

### flash

1. The problem statement, all variables and given/known data
Find the angle between the line x=7 and the catenary $$y=20\cosh{(\frac{x}{20})}-15$$

3. The attempt at a solution

I found the tangent has gradient $$\sinh{(\frac{7}{20})}$$

Then I used $$\tan{\theta}=|\frac{1}{m}|$$
where $$m=\sinh{(\frac{7}{20})}$$

And evaluated using inverse tan on my calculator.

I'm pretty sure we aren't meant to use a calculator though, so my question is can the inverse tan of that be evaluated manually somehow?

Thanks

2. Apr 27, 2008

### HallsofIvy

Staff Emeritus
If you "aren't meant to use a calculator" then give, as your answer,
$$tan^{-1}(\frac{1}{sinh(7/20)})$$
There is no simple way to calculate a numerical solution.