Question

Hi, can you help me to solve this exercise please!!

Answer 1

It is given that

$\csc (\theta)=\frac{\sqrt[]{170}}{10}$

We know that

$\sin (\theta)=\frac{1}{\csc (\theta)}$

$\text{Substitute }\csc (\theta)=\frac{\sqrt[]{170}}{10},\text{ we get}$

$\sin (\theta)=\frac{1}{\frac{\sqrt[]{170}}{10}}$

$\sin (\theta)=\frac{10}{\sqrt[]{170}}$

$\sin (\theta)=\frac{\sqrt[]{10}\sqrt[]{10}}{\sqrt[]{17\times10}}$

$\sin (\theta)=\frac{\sqrt[]{10}}{\sqrt[]{17}}$

$\sin (\theta)=\sqrt[]{\frac{10}{17}}$

Hence the required value is

$\sin (\theta)=\sqrt[]{\frac{10}{17}}$