Question 1079670
<pre>
I like to explain why, when possible, not just spout formulas.

Here's why!

Draw this simple picture.

{{{drawing(200,100,-.5,2,-.5,1.5,line(-3,0,3,0),line(0,-3,0,3), line(0,0,1.5,1),line(1.5,0,1.5,1),locate(.4,.3,theta), locate(1.53,.62,y),locate(.77,0.05,x),locate(.75,.85,r) )}}} 

{{{sin(theta)=opposite/hypotenuse}}}

{{{sin(theta)=y/r}}}

{{{ y = 4 }}}  <-- given

Substitute 4 for y

{{{sin(theta)=4/r}}}

Solve for r

{{{sin(theta)/1=4/r}}}

Cross multiply

{{{r*sin(theta)=4}}}

{{{r=4/sin(theta)}}}

Edwin</pre>