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find tan 30 degrees and tan 45 degrees using the 45-45-90 triangle therom and 30-60-90 triangle theorm

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[tex]tan30^o=\frac{\frac{a}{2}}{\frac{a\sqrt3}{2}}=\frac{a}{2}\cdot\frac{2}{a\sqrt3}=\frac{1}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{\sqrt3}{3}\\\\\\tan45^o=\frac{a}{a\sqrt2}=\frac{1}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{\sqrt2}{2}[/tex]
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