Question

Find the length of side x in simplest radical form with a rational denominator v5

Answer 1

Determine the value of x by using the trigonometric ratio for the triangle.

`\begin{gathered} \sin 45^(\circ)=\frac{x}{\sqrt[]{5}} \\ \frac{1}{\sqrt[]{2}}=\frac{x}{\sqrt[]{5}} \\ x=\frac{\sqrt[]{5}}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =\frac{\sqrt[]{10}}{2} \end{gathered}`

So length of side x is,

`\frac{\sqrt[]{10}}{2}`