To solve this problem, we can use trigonometric functions. The given right triangle has an angle of $31^\circ$, the hypotenuse (18), and we are asked to find the adjacent side, $x$.

Since we know the angle and the hypotenuse, we can use the cosine function:

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

$\cos(31^\circ) = \frac{x}{18}$

Now, solving for $x$:

$x = 18 \times \cos(31^\circ)$

I'll calculate this for you.The length of the missing side $x$ is approximately $15.4$ units, rounded to the nearest tenth.

Would you like further details or explanations?

Here are some related questions you might find helpful:

1. How can I solve for the opposite side using sine?
2. What are the other trigonometric ratios for this triangle?
3. How do you solve a triangle with two known sides and an angle?
4. What is the relationship between the sine and cosine of complementary angles?
5. How can I use the Pythagorean theorem in this case?

Tip: For angle problems, it's often helpful to remember which trigonometric function relates the known sides and the angle.