Explanation
Given triangle PQR:
[tex]\begin{gathered} \sin P=\frac{x}{r}\text{ } \\ \text{S}o\text{ }x=r\sin P \end{gathered}[/tex][tex]\begin{gathered} \sin R=\frac{x}{p}\text{ } \\ So\text{ }x=p\sin R \end{gathered}[/tex]
Setting the two expressions equal to each other gives the equation:
[tex]r\sin P=p\sin R[/tex]
Divide both sides of the equation by pr to give the result:
[tex]\begin{gathered} \frac{r\sin P}{pr}=\frac{p\sin R}{pr} \\ \\ \frac{\sin P}{p}=\frac{\sin R}{r} \end{gathered}[/tex]
