Question

Need help with 3,4,5,and 6 please. I don’t understand it

Answer 1

4. The triangle has 3 given sides but no angles but we can get the angles using cosine law

`\begin{gathered} \cos R=(t^2+s^2-r^2)/(2ts) \\ \cos \text{ R=}(23.7^2+48^2-35^2)/(2*23.7*48) \\ \cos R=(561.69+2304-1225)/(2275.2) \\ \cos R=(1640.69)/(2275.2) \\ \cos R=0.7211190225 \\ R=\cos ^(-1)0.7211190225 \\ R=43.8530535482 \\ R=44^(\circ) \end{gathered}`
`\begin{gathered} \cos T=(r^2+s^2-t^2)/(2rs) \\ \cos T=(35^2+48^2-23.7^2)/(2*35*48) \\ \cos T=(1225+2304-561.69)/(3360) \\ \cos T=(3529-561.69)/(3360) \\ \cos T=(2967.31)/(3360) \\ \cos T=0.88312797619 \\ T=\cos ^(-1)0.88312797619 \\ T=27.977977493 \\ T=28^(\circ) \end{gathered}`
`\begin{gathered} S=180-28-44 \\ S=108^(\circ) \end{gathered}`

From largest to smallest it will be

`\angle S,\angle R\text{ and}\angle T`