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Sagot :
The cosine of an angle can be expressed as,
[tex]\begin{gathered} \cos \text{ a=}\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \cos a=\frac{1}{2} \end{gathered}[/tex]From above equation, we can take adjacent side=1 and hypotenuse =2.
Using pythagorus theorem,
[tex]\begin{gathered} \text{hypotenuse}^2=oppositeside^2+adjacentside^2 \\ 2^2=oppositeside^2+1^2 \\ 4=oppositeside^2+1^{} \\ 3=oppositeside^2 \\ \sqrt[]{3}=oppositeside^{} \end{gathered}[/tex]Now, the tan of a is,
[tex]\begin{gathered} \tan a=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan a\text{ =}\frac{\sqrt[]{3}}{1} \\ \tan a=\sqrt[]{3} \end{gathered}[/tex]METHOD 2
cos a=1/2. cos function has 1/2 as value when a=60 degrees.
So, a=60.
[tex]\tan a=\tan 60^{\circ}=\sqrt[]{3}[/tex]
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