$\cos \left( \dfrac{I}{2} \right) = \dfrac{R}{R + E}$
$\cos 18^\circ 15' = \dfrac{R}{R + 12.02}$
$R \cos 18^\circ 15' + 12.02 \cos 18^\circ 15' = R$
$R - R \cos 18^\circ 15' = 12.02 \cos 18^\circ 15'$
$R(1 - \cos 18^\circ 15') = 12.02 \cos 18^\circ 15'$
$R = \dfrac{12.02 \cos 18^\circ 15'}{1 - \cos 18^\circ 15'}$
$R = 226.94 \, \text{ m}$ [ C ] answer