For the next two (02) items that follow : The angles \(A\), \(B\) and \(C\) of a triangle \(ABC\) are in the ratio \(1:2:7\).
What is the ratio of the side of greatest length to the side of least length?
\((3+\sqrt{5}):2\)
Since \(A:B:C=1:2:7\) and \(A+B+C=180°\), we get \(A=18°\), \(B=36°\), \(C=126°\). By the sine rule the sides are proportional to \(\sin A,\sin B,\sin C\), so the ratio of greatest side (opposite \(C\)) to least side (opposite \(A\)) is \(\sin126°:\sin18°=\sin54°:\sin18°=\dfrac{(\sqrt5+1)/4}{(\sqrt5-1)/4}=(3+\sqrt5):2\).
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