The given triangle is a right angle triangle. Taking angle 30 degrees as the reference angle,
opposite side = square root of 2
adjacent side = x
We would find the value of x by applying the tangent trigonometric ratio which is expressed as
tan# = opposite side/adjacent side
Recall
[tex]\tan \text{ 30 = }\frac{1}{\sqrt[]{3}}[/tex]
Thus, we have
[tex]\begin{gathered} \tan \text{ 30 = }\frac{\sqrt[]{2}}{x} \\ By\text{ crossmultiplying,} \\ x\tan 30\text{ = }\sqrt[]{2} \\ x\text{ }\times\text{ }\frac{1}{\sqrt[]{3}}\text{ = }\sqrt[]{2} \\ \frac{x}{\sqrt[]{3}}=\text{ }\sqrt[]{2} \\ x\text{ = }\sqrt[]{2}\text{ }\times\text{ }\sqrt[]{3} \\ x\text{ = }\sqrt[]{6} \end{gathered}[/tex]
