I have just built a house and have a home theater whose back wall is
curved.  It faces the corner of a room where a Television will go.  I
am trying to purchase two things - a curtain track and furniture that
will "curve" in the shape of the rear wall.  I have made two measures
- The straight line distance to the ends of each section of the curved
wall (its 213" long) and then at the mid point on this string ran a
line @ a 90 degree angle to the edge of the arc in the back wall
(29").  I am stuck - how do I find the length of the arc and how do I
find the "angle" (or is it radians) of this arc?  Simply put I need to
tell the curtain guy how long the track is and how much to bend it and
I need to tell the furnuture guy how to cut the angles in the armrests
of the recliners to ensure the furniture nicely fits the curve of the
room.

Perhaps the answer to this question can help:
http://answers.google.com/answers/threadview?id=443143

But maybe someone still needs to tell how to calculate the length of the wall.

Be sure to measure carefully and to let the guy doing the curtain
track how far from the wall it should be, i.e., a smaller radius than
that of the wall.

This site

http://www.1728.com/circsect.htm

lets you calculate the values you want. In regards to circle two shown
in that site, you have the chord AB (213") and the segment height
(29"). To do the calculation, click on the "Chord & Segment Height"
under "Click on the 2 variables you know." Then fill in 213 after
"Chord AB" and 29 after "Segment Height ED."

The arc length is shown as 223.38 and the central angle is 60.929.

As I imagine it, the angle for the armrests would only fit the 60.9
degree angle if the furniture extended along the entire length of the
curved wall.

Search strategy: chord height arc length

Regarding the furniture: If the furniture has a curved back that
follows the curve of the room, the angle of each armrest will be 90
degrees from a tangent to the back at the ends. If the furniture has a
straight back and it extends along the chord you measured, the angle
for each armrest will be 59.535 degrees from the back. (I got the
59.535 degrees from the triangle formed by the chord and two radii;
since the central angle is 60.929, the remaing two angles are (180 -
60.929)/2.)

I think I'm missing something about the construction of the furniture,
though; but I suspect the furniture maker will know how to make what
you want from the arc length and the central angle.

Assuming that the arc you are talking about is a circular arc, you
have been given good advice.

If this is not the case, you need specify what kind of an arc or curve
you are talking about.

Upon a careful reading of the question, I agree with Brix24, that
there is some ambiguity in exactly how the furniture is laid out.  Be
sure to check with your furniture guy.

Myoarin also has a good point.  The arc length calculated by Brix24 is
the length of a chalk line on the wall.  I looked at my curtain rod
and it is a little over three inches from the wall.  In that case you
would have a slightly shorter length and a little tighter curve (bend)
in the rod because the radius of the arc is shorter.

You can get an idea of how close the curve is to a circle by measuring
two additional straight lines. If I refer your measurements to circle
two at

http://www.1728.com/circsect.htm

you have measured distances AB and ED. If you draw in two additional
chords, AD and DB, their lengths should be 110.38 inches each.

[The 110.38 is from the Pythogorean theorem: The triangle AED is a
right triangle, with AD= square root ( (c/2)^2 + h^2), where c =
distance AB = 213 and h = distance ED = 29].

The further these values are from each other or from 110.38, the
greater the departure of the curve from a circle. You can see some of
this by imagining that "circle two" is pulled vertically into an
ellipse, but keeping A, B, and D on the arc; the distances AD and DB
become longer than 110.38. Similarly, if the circle is stretched out
horizontally, the distances AD and DB become shorter than 110.38 each.

Guys, This is not a mathmatical question, this is a furniture
question.  And a custom furniture question at that.

Get the furniture guy and the curtain guy to come to the house.  Point
to the wall where the stuff goes and describe as acurrately as
possible what you expect to see when everything is installed.  Ask
each tradesperson to  make as many measurements has he or she needs. 
Ask for a drawing with dimensions.

When you are satisfied that the drawing accurately describes your
expectations, tell the tradesperson to make the furniture or curtain.

The responsibility for making things fit should be theirs not yours. 
If you do the measurements and provide the drawing, then you are stuck
with an
expensive piece of furniture that does not fit.

I think that Phil is right, practically speaking.  Wish that had occurred to me.:)

I need to retract my statement about using the Pythagorean theorem to
indicate how close the curve is to a circle. Upon further reflection,
this will hold true whether the curve is part of a circle or certain
parts of ellipses. I suspect that additional points on the curve would
need to be referenced to distinguish a circle from another smooth
curve.

In following philnj's advice, you might still be careful to evaluate
the expertise of the curtain maker and the furniture maker. You will
probably have to put down half the price of the items in advance, and
a maker could still raise a dispute if something goes wrong. It might
be safer to have the curtain rods made first; major mistakes there are
probably less expensive than furniture mistakes; and learning from
that experience might help with the furniture.