# What is the length of an arch whose top height is 4 foot above a 20 foot span?

End to end on this building it's 20 feet. So If I build an arch that bows to a top height of 4 feet.. What is the length of that arch? ( i know this isn't rocket science but it is to me !)

### 3 Answers

- Mr. Un-couthLv 77 years agoFavorite Answer
Length of the arc = 21.9912 feet

The average radius for 90 degrees = 4' + [(10` - 4`)/2] = 7 Feet

Circumference of complete circle with 7 foot radius = (2pi)*(radius) = (6.2832)*(7`) =43.9824 ft

Length of a 180` arc with a 7' radius = 43.09824`/2 = 21.9912 feet

Note: This is my guess at how to solve the problem. My answer may not be precise but it should be a decent estimate if not exact.

- Tony RBLv 77 years ago
Several arches are listed with photographs in this Wikipedia about arches :

http://en.wikipedia.org/wiki/Arch

along with links to other articles about specific arches, but I doubt they include calculations for determining length of each arch.

You might have to consult your arch enemy for more information.

- Anonymous7 years ago
Unless your "arch" has a specific curve to it there is no way to answer your question.