Question 1082990
The formula we'll use is
{{{s = theta*r}}}


where 
s = arc length
{{{theta}}} (greek letter theta) = angle in radians ** see <font color=blue>note</font> below **
r = radius


We're given 
s = 15 inches
{{{theta = 2.5}}} radians


and we want to find r


<font color=blue>Note</font>: The angle MUST be in radians for this formula to work. If the angle is in degrees, you need to convert to radians first. Or if you want to keep theta in degree mode, you can use the formula {{{s = (theta/360)*2*pi*r}}} which is a bit more complicated. 


----------------------------------------------------------------------


Plug the two given items into the formula and solve for r (divide both sides by 2.5)


{{{s = theta*r}}}


{{{15 = 2.5*r}}}


{{{15/2.5 = (2.5*r)/2.5}}}


{{{6 = r}}}


{{{r = 6}}}


----------------------------------------------------------------------
----------------------------------------------------------------------


So <font color=red>the radius is 6 inches</font>