Question

Complete the derivation of the law of sines for PQR

Answer 1

Step-by-step explanation

Given triangle PQR:

`\begin{gathered} \sin P=(x)/(r)\text{ } \\ \text{S}o\text{ }x=r\sin P \end{gathered}`
`\begin{gathered} \sin R=(x)/(p)\text{ } \\ So\text{ }x=p\sin R \end{gathered}`

Setting the two expressions equal to each other gives the equation:

`r\sin P=p\sin R`

Divide both sides of the equation by pr to give the result:

`\begin{gathered} (r\sin P)/(pr)=(p\sin R)/(pr) \\ \\ (\sin P)/(p)=(\sin R)/(r) \end{gathered}`