Question

Find the length of side x in simplest radical form with a rational denominator.45х45V3

Answer 1

`x=\frac{2\sqrt[]{3}}{\sqrt[]{2}}`

Step-by-step explanation

Step 1

we have a right triangle,Let

`\begin{gathered} \text{angle}=45 \\ \text{adjacent side=}\sqrt[]{3} \\ \text{Hypotenuse=x} \\ \cos \text{ 45=}\frac{\sqrt[]{2}}{2} \end{gathered}`

use cosinbe function

`\begin{gathered} \cos \alpha=\frac{adjancen\text{ side}}{\text{hypotenuse}} \\ \text{isolating hypotenuse} \\ \cos \alpha\cdot hypote\\u se=\text{adjancent side} \\ \text{Hypotenuse}=\frac{adjancent\text{ side}}{\cos\alpha} \\ \text{replace} \\ x=\frac{\sqrt[]{3}}{\cos45} \\ x=\frac{\frac{\sqrt[]{3}}{1}}{\frac{\sqrt[]{2}}{2}} \\ x=\frac{2\sqrt[]{3}}{\sqrt[]{2}} \end{gathered}`

I hope this helps you