Identify the known values and the unknown value in the right-angled triangle.

We are given:

• An angle $\theta = 40^\circ$.
• The side adjacent to the $40^\circ$ angle is 8.
• The side opposite to the $40^\circ$ angle is $x$.

The tangent function relates the opposite side, the adjacent side, and the angle:

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$

Multiply both sides by 8:

$$x = 8 \times \tan(40^\circ)$$

Using a calculator for $\tan(40^\circ)$:

$$\tan(40^\circ) \approx 0.8391$$ $$x = 8 \times 0.8391$$ $$x \approx 6.7128$$

$$x \approx 6.71$$

The value of $x$ is:

$$\text{6.71}$$