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

Put the angles in the triangle in order from least to greatest-example-1
User Treng
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1 Answer

15 votes
15 votes

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)

User Dt Dino
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