Question

find the length of side x in simplest radical form with a rational denominator. 30° 1 60° x answer attempt 2 out of 2 x - √5 / 2 submit answer

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, for an angle of \(60^{\circ}\), we know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 60^{\circ}\), the opposite side is \(x\) and the hypotenuse is \(1\). So, \(\sin60^{\circ}=\frac{x}{1}\).

Step2: Calculate \(\sin60^{\circ}\)

We know that \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\). Since \(\sin60^{\circ}=\frac{x}{1}\), then \(x = \sin60^{\circ}\).

Answer:

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