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The image shows a right-angled triangle with one of the non-right angles labeled as \(69^\circ\). The side opposite this angle is marked as \(a\), and we can assume that you are asked to find the length of side \(a\) relative to the other sides or angles of the triangle.

To solve for \(a\), we can apply trigonometric principles. Since we have a right triangle and we know an angle (other than the right angle) and need to find a side, the sine function is appropriate because it relates the opposite side and the hypotenuse. The sine function is defined as:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case:
- \(\theta = 69^\circ\)
- The side opposite the angle \(69^\circ\) is \(a\)
- Let the hypotenuse be denoted as \(c\).

So:
\[
\sin(69^\circ) = \frac{a}{c}
\]

Thus, to find \(a\), we multiply both sides by \(c\):
\[
a = c \cdot \sin(69^\circ)
\]

To proceed further, we would need the length of the hypotenuse (\(c\)).

Would you like more details on this, or do you know the length of the hypotenuse so we can calculate \(a\)?

Here are 5 related questions to expand on this concept:
1. How do we calculate the length of the adjacent side using trigonometric functions?
2. What is the cosine function and how could it be used in this problem?
3. How would you solve for \(a\) if the hypotenuse were unknown?
4. What are the other angles of the triangle if one angle is \(69^\circ\)?
5. How can you apply the Pythagorean theorem to check the solution?

**Tip:** Always make sure the angle you are using matches the side you're solving for in trigonometric problems (opposite, adjacent, or hypotenuse).

Find the length of side 'a' given a right triangle with an angle of 69 degrees.

This problem involves finding the length of side 'a' in a right triangle using trigonometric functions. Given a 69-degree angle and the hypotenuse, you can apply the sine function to solve for the opposite side.

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