Question

Find the length of side x in simplest radical form with a rational denominator.60°V230°х

Answer 1

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

`\tan \text{ 30 = }\frac{1}{\sqrt[]{3}}`

Thus, we have

`\begin{gathered} \tan \text{ 30 = }\frac{\sqrt[]{2}}{x} \\ By\text{ crossmultiplying,} \\ x\tan 30\text{ = }\sqrt[]{2} \\ x\text{ }*\text{ }\frac{1}{\sqrt[]{3}}\text{ = }\sqrt[]{2} \\ \frac{x}{\sqrt[]{3}}=\text{ }\sqrt[]{2} \\ x\text{ = }\sqrt[]{2}\text{ }*\text{ }\sqrt[]{3} \\ x\text{ = }\sqrt[]{6} \end{gathered}`