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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?

What is the value of cos(θ) for a triangle with sides 4, 5, and 6?

Explore how to calculate cos(θ) in a triangle with sides 4, 5, and 6. This detailed explanation covers key trigonometric concepts, including the cosine rule and the application of cos(θ) = adjacent / hypotenuse. Ideal for students in Grades 9-12.

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