Question

question
find the length of side ( x ) in simplest radical form with a rational denominator.
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), adjacent side \(= 2\), and hypotenuse \(=x\). So \(\cos30^{\circ}=\frac{2}{x}\).
Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(\frac{\sqrt{3}}{2}=\frac{2}{x}\).

Step2: Solve for \(x\)

Cross - multiply: \(x\times\sqrt{3}=2\times2\). Then \(x = \frac{4}{\sqrt{3}}\).
Rationalize the denominator: \(x=\frac{4\sqrt{3}}{3}\).

Answer:

\(\frac{4\sqrt{3}}{3}\)