check the picture below.
notice, the width is the cosine and the length is the sine.
[tex]\bf sin(60^o )=\cfrac{y}{47}\implies 47\cdot sin(60^o)=y\implies 47\cdot \cfrac{\sqrt{3}}{2}=y
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\cfrac{47\sqrt{3}}{2}=\stackrel{length}{y}\\\\
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cos(60^o )=\cfrac{x}{47}\implies 47\cdot cos(60^o)=x\implies 47\cdot \cfrac{1}{2}=x
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\cfrac{47}{2}=\stackrel{width}{x}\\\\
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x\cdot y\implies \cfrac{47\sqrt{3}}{2}\cdot \cfrac{47}{2}\implies \cfrac{2209\sqrt{3}}{4}\impliedby \textit{area of the mirror}[/tex]
