This is a right triangle where we are tasked with finding the length of side $PQ$, labeled as $x$. You have the following information:

• The hypotenuse $RQ = 13$
• The angle $\angle PQR = 48^\circ$
• The side adjacent to the angle is $PQ = x$

We can solve for $PQ$ using the cosine function, because cosine of an angle in a right triangle is defined as:

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Thus, we can write:

$\cos(48^\circ) = \frac{PQ}{13}$

Now, solving for $PQ$:

$PQ = 13 \cdot \cos(48^\circ)$

Using a calculator:

$PQ = 13 \cdot 0.6691 \approx 8.7$

So, the length of side $PQ$ is approximately 8.7 units.

Would you like further explanation or additional questions? Here are some related topics you might find interesting:

1. How to use sine and tangent for solving right triangles
2. How to solve for unknown angles in a right triangle
3. Applications of trigonometric ratios in real-world problems
4. Deriving the trigonometric ratios from a right triangle
5. Pythagorean Theorem and its relation to trigonometry

Tip: When solving for unknown sides or angles, always check if your calculator is set to degrees or radians!