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 trigonometric ratio

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 60^{\circ}\), adjacent side \(=\sqrt{7}\), and hypotenuse \(=x\). So \(\cos60^{\circ}=\frac{\sqrt{7}}{x}\).
Since \(\cos60^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{\sqrt{7}}{x}\).

Step2: Solve for \(x\)

Cross - multiply: \(x = 2\sqrt{7}\).

Answer:

\(x = 2\sqrt{7}\)