Question 552827
"The central angle pheta of a circle with radius 9 inches intercepts an arc of 20 inches. Find pheta to the nearest degree."  Thats the problem word for word, any help is strongly appreciated.
<pre>
The Greek letter <font face = "symbol">q</font> is "theta", not "pheta". <font face="wingdings">J</font>

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

{{{drawing(350,350,-1.5,1.5,-1.5,1.5,

green(arc(0,0,2,-2,63.66197724,296.3380228)),
red(arc(0,0,2,-2,296.3380228,423.6619772)),red(arc(0,0,.5,-.5,296.3380228,423.6619772),

line(0,0,cos(10/9),sin(10/9)), line(0,0,cos(10/9),-sin(10/9))),
red(locate(1.05,0,s=20in)),red(locate(.1,.05,theta),locate(-.2,.5,r=9in))

 )}}}

The formula for <font face = "symbol">q</font> in radians, not degrees, is 

<font face = "symbol">q</font> = {{{s/r}}} 

where s = the arc length and r = the radius.

So in radians

<font face = "symbol">q</font> = {{{20in/(9in)}}} = {{{20/9}}}(radians)

To convert radians to degrees, we multiply by {{{"180°"/pi}}}

{{{expr(20/9)expr("180°"/pi)}}} = 127.3239545°

To the nearest degree: 127°

Edwin</pre>