Find the length of side x in the given triangle.

The sum of angles in a triangle is $180^\circ$. Let the unknown angle be $\theta$.

This means the triangle is a right-angled triangle.

Let the angle opposite side $x$ be $30^\circ$.
Let the angle opposite the side 8 cm be $90^\circ$. This means 8 cm is the hypotenuse.
We need to find $x$, which is the side opposite the $30^\circ$ angle.

The sine of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

For the $30^\circ$ angle:

We know that $\sin(30^\circ) = \frac{1}{2}$.

Multiply both sides by 8:

The unit for $x$ is cm.

The value of $x$ is 4 cm.