We need to find the length of side $x$ in the given right triangle. The triangle has angles of 30, 60, and 90 degrees. The hypotenuse is of length 4. The side $x$ is adjacent to the 60 degree angle. We need to express the answer in simplest radical form with a rational denominator.

1. Problem Description

We need to find the length of side $x$ in the given right triangle. The triangle has angles of 30, 60, and 90 degrees. The hypotenuse is of length

4. The side $x$ is adjacent to the 60 degree angle. We need to express the answer in simplest radical form with a rational denominator.

2. Solution Steps

Since we have a 30-60-90 triangle, we can use trigonometric ratios to find the length of the side $x$. Since $x$ is adjacent to the 60-degree angle and the hypotenuse is 4, we can use the cosine function:

$cos(60^{\circ}) = \frac{adjacent}{hypotenuse}$

$cos(60^{\circ}) = \frac{x}{4}$

We know that $cos(60^{\circ}) = \frac{1}{2}$, so we can write:

$\frac{1}{2} = \frac{x}{4}$

Multiply both sides by 4 to solve for $x$:

$x = 4 \cdot \frac{1}{2} = 2$

3. Final Answer

$x = 2$