The triangle in the image provided appears to be a right-angled triangle, with sides labeled as 4, 5, and 6 units. Given that we need to find $\cos \theta$, where $\theta$ is the angle adjacent to the side of length 6, we will apply the cosine definition.

Step-by-step solution:

In a right triangle, cosine is defined as:

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

Here:

• The side adjacent to $\theta$ is the one labeled as 6 units.
• The hypotenuse is the longest side, which is labeled as 5 units.

Therefore:

$\cos \theta = \frac{6}{5}$

However, this result is problematic because in a right triangle, the hypotenuse must be the largest side, which should be larger than both 4 and 6. Thus, it seems that the triangle may not be right-angled as drawn.

To clarify:

• This triangle might not follow the Pythagorean theorem (as $5^2 \neq 6^2 + 4^2$).
• It could be a more general triangle, in which case we would use the cosine rule to determine $\cos \theta$.

Would you like me to apply the cosine rule or clarify further?