Find $\mathrm{sin}\frac{\theta}{2}$ when $\mathrm{sin}\theta =\frac{35}{}$ , and $0}^{\circ}<\theta <{90}^{\circ$

The answer I'm currently getting is$\sqrt{\frac{1}{10}}$ but the answer must be either $\frac{\sqrt{10}}{10},\frac{3\sqrt{10}}{10}\text{}\text{or}\text{}\frac{13}{}$

My Process:

since$\mathrm{sin}\frac{\theta}{2}=\pm \sqrt{\frac{1-\mathrm{cos}\theta}{2}}$

$\sqrt{\frac{1-\frac{4}{5}}{2}}\cdot \sqrt{\frac{5}{5}}=\sqrt{\frac{5-4}{10}}=\sqrt{\frac{1}{10}}$

The answer I'm currently getting is

My Process:

since