It is given that
[tex]\csc (\theta)=\frac{\sqrt[]{170}}{10}[/tex]
We know that
[tex]\sin (\theta)=\frac{1}{\csc (\theta)}[/tex]
[tex]\text{Substitute }\csc (\theta)=\frac{\sqrt[]{170}}{10},\text{ we get}[/tex]
[tex]\sin (\theta)=\frac{1}{\frac{\sqrt[]{170}}{10}}[/tex]
[tex]\sin (\theta)=\frac{10}{\sqrt[]{170}}[/tex]
[tex]\sin (\theta)=\frac{\sqrt[]{10}\sqrt[]{10}}{\sqrt[]{17\times10}}[/tex]
[tex]\sin (\theta)=\frac{\sqrt[]{10}}{\sqrt[]{17}}[/tex]
[tex]\sin (\theta)=\sqrt[]{\frac{10}{17}}[/tex]
Hence the required value is
[tex]\sin (\theta)=\sqrt[]{\frac{10}{17}}[/tex]
