Angle between catenary and line

[flash]

Homework Statement

Find the angle between the line x=7 and the catenary y=20\cosh{(\frac{x}{20})}-15

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

 

[HallsofIvy]

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.