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 \(\sin A\cdot\cos B\) equal to?
\(1/4\)
With \(A=18°\) and \(B=36°\), \(\sin18°=\dfrac{\sqrt5-1}{4}\) and \(\cos36°=\dfrac{\sqrt5+1}{4}\), so \(\sin A\cdot\cos B=\dfrac{(\sqrt5-1)(\sqrt5+1)}{16}=\dfrac{5-1}{16}=\dfrac{1}{4}\).
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