Let us draw out the triangle below:
Given that
[tex]\arctan \frac{\sqrt[]{3}}{3}=\beta[/tex]
Using the trigonometric identity for tan 30, where
[tex]\tan 30=\frac{\sqrt[]{3}}{3}[/tex]
Therefore,
[tex]\beta=30\degree[/tex]
The sum of angles in a triangle is 180°.
Therefore,
[tex]\begin{gathered} \alpha+\beta+90=180\degree \\ \therefore \\ \alpha+30+90=180 \\ \alpha=180-90-30 \\ \alpha=60\degree \end{gathered}[/tex]
To get the sides of the triangle, let us apply the Trigonometric ratios:
Using the Sine Trig. ratio,
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