Question

find the length of side x in simplest radical form with a rational denominator.

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse is \(1\), and the side opposite to \(30^{\circ}\) is \(x\). But we can also use \(\sin60^{\circ}=\frac{x}{1}\) (since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\)).

$$x = \sin60^{\circ}\times1$$

Step2: Simplify the expression

We know that \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\).

Answer:

\(x=\frac{\sqrt{3}}{2}\)