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Determine the value of 
cos
⁡
(
θ
)
cos(θ)
 by identifying the correct ratio:

To determine \(\cos(\theta)\) in the given right triangle, we need to use the definition of the cosine function in a right triangle. The cosine of an angle \(\theta\) is given by the ratio of the length of the adjacent side to the hypotenuse.

From the triangle:

- The side adjacent to \(\theta\) is \(12\).
- The hypotenuse is \(15\).

Thus, the cosine of the angle \(\theta\) is:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{15}
\]

We can simplify this fraction:

\[
\cos(\theta) = \frac{12}{15} = \frac{4}{5}
\]

So, \(\cos(\theta) = \frac{4}{5}\).

Would you like more details or have any questions?

Here are some related questions:
1. How would you find \(\sin(\theta)\) for the same triangle?
2. What is the value of \(\tan(\theta)\) in this triangle?
3. Can you determine the length of the side opposite to \(\theta\) using trigonometry?
4. How would you verify the Pythagorean theorem with the sides provided?
5. How would you find the area of this right triangle?

**Tip:** Remember, when solving right triangles, always identify which side is adjacent, opposite, and hypotenuse relative to the angle in question.

Learn how to determine the value of cos(θ) in a right triangle using trigonometry. This problem involves applying the cosine function to find the ratio of the adjacent side to the hypotenuse in a specific triangle. Suitable for high school students in Grades 10-12.

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