Question

Put the angles in the triangle in order from least to greatest

Answer 1

Given:

`ST=17,SR=18,RT=12`

Use the cosine rule,

`\begin{gathered} RT^2=ST^2+SR^2-2(ST)(SR)\cos S \\ 12^2=17^2+18^2-2(17)(18)\cos S \\ \cos S=(469)/(612) \\ S=\cos ^(-1)((469)/(612)) \\ S=39.97^(\circ) \end{gathered}`

And,

`\begin{gathered} ST^2=SR^2+RT^2-2(SR)(RT)\cos R \\ 17^2=18^2+12^2-2(18)(12)\cos R \\ \cos R=(179)/(432) \\ R=\cos ^(-1)((179)/(432)) \\ R=65.52^(\circ) \end{gathered}`

Also,

`\begin{gathered} \angle S+\angle R+\angle T=180^(\circ) \\ 39.97^(\circ)+65.52^(\circ)+\angle T=180^(\circ) \\ \angle T=180^(\circ)-39.97^(\circ)-65.52^(\circ) \\ \angle T=74.51^(\circ) \end{gathered}`

So, the order of angles from least to greatest is,

`\angle S,\angle R,\angle T`

Answer: option c)