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,

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

And,

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

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)