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The given triangle is a right triangle, with sides labeled as follows:

- The hypotenuse is \( 15 \).
- The side adjacent to the angle \( \theta \) is \( 9 \).

We can use the cosine function to find the angle \( \theta \), since cosine relates the adjacent side and the hypotenuse in a right triangle.

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9}{15} = 0.6
\]

Now, to find \( \theta \), we use the inverse cosine (cos⁻¹):

\[
\theta = \cos^{-1}(0.6)
\]

Calculating this:

\[
\theta \approx 53.1^\circ
\]

Thus, the value of angle \( \theta \) is approximately **53.1°**.

Would you like more details on the steps, or do you have any questions?

Here are some related questions you might explore:

1. How do the sine and tangent values of \( \theta \) compare to cosine?
2. What are the remaining angles in the triangle?
3. How does the Pythagorean theorem confirm the side lengths?
4. What would the angle \( \theta \) be if the adjacent side were different?
5. Can we derive \( \theta \) using other trigonometric identities?

**Tip**: In right triangles, always remember that the sum of all angles equals \( 180^\circ \), with the right angle being \( 90^\circ \).

What is the value of the angle theta in a right triangle with a hypotenuse of 15 and an adjacent side of 9?

Learn how to calculate the angle theta in a right triangle where the hypotenuse is 15 and the adjacent side is 9. This problem involves trigonometric concepts and the cosine function, ideal for students in Grades 9-12.

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