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The problem you've uploaded appears to involve a trigonometric calculation, specifically dealing with angles in a right triangle. Here's a breakdown of the image:

### Problem Statement:
1. **Diagram**: The image shows a right triangle, where:
   - The hypotenuse is labeled as 10 units.
   - The adjacent side is 6 units.
   - The angle \(\theta\) opposite the unknown side is the angle you need to find.

2. **Task**: You are asked to find the value of the angle \(\theta\).

3. **Options**:
   - \( \theta = 30^\circ \)
   - \( \theta = 45^\circ \)
   - \( \theta = 53^\circ \)
   - \( \theta = 60^\circ \)

### Solution:
To solve for the angle \(\theta\), we can use the cosine function, which relates the adjacent side to the hypotenuse:

\[
\cos(\theta) = \frac{\text{Adjacent Side}}{\text{Hypotenuse}} = \frac{6}{10} = 0.6
\]

Now, find the angle \(\theta\) using the inverse cosine function:

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

Let's calculate this.

The angle \(\theta\) is approximately \(53.13^\circ\). Therefore, the correct answer is:

\[
\theta = 53^\circ
\]

Would you like further details on this solution or have any questions?

Here are five related questions to expand on this concept:

1. How do you determine the other angle in a right triangle if one angle is known?
2. What is the sine of angle \(\theta\) in this triangle?
3. Can you find the length of the opposite side using the tangent function?
4. How would the angle change if the hypotenuse was longer?
5. What is the relationship between the sine, cosine, and tangent functions for an angle?

**Tip**: When working with trigonometric functions, always ensure your calculator is set to the correct mode (degrees or radians) based on the problem requirements.

Find the angle \(\theta\) in a right triangle where the hypotenuse is 10 units, the adjacent side is 6 units, and you are given multiple-choice options for the angle.

Learn how to find the angle \(\theta\) in a right triangle using the cosine function. This problem involves a right triangle where the hypotenuse is 10 units and the adjacent side is 6 units. Suitable for students in Grades 9-10.

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