Solve for r
\left\{\begin{matrix}r=\frac{S}{2\sin(\frac{\alpha }{2})}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =2\pi n_{1}\\r\in \mathrm{R}\text{, }&S=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\alpha =2\pi n_{1}\end{matrix}\right.
Solve for S
S=2r\sin(\frac{\alpha }{2})
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2r\sin(\frac{\alpha }{2})=S
Swap sides so that all variable terms are on the left hand side.
2\sin(\frac{\alpha }{2})r=S
The equation is in standard form.
\frac{2\sin(\frac{\alpha }{2})r}{2\sin(\frac{\alpha }{2})}=\frac{S}{2\sin(\frac{\alpha }{2})}
Divide both sides by 2\sin(\frac{1}{2}\alpha ).
r=\frac{S}{2\sin(\frac{\alpha }{2})}
Dividing by 2\sin(\frac{1}{2}\alpha ) undoes the multiplication by 2\sin(\frac{1}{2}\alpha ).
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