https://file.aiquickdraw.com/mathbot/file/1727790969830yl8ip2lc.jpg

The image shows a right-angled triangle with the following details:

- One angle is \(30^\circ\).
- The hypotenuse is labeled as 15 meters.
- The adjacent side (horizontal) is labeled as \(x\).
- The opposite side (vertical) is labeled as \(y\).

To solve for \(x\) and \(y\), we can use trigonometric ratios:

1. **For \(x\) (adjacent side)**:
   \[
   \cos(30^\circ) = \frac{x}{15}
   \]
   Solving for \(x\):
   \[
   x = 15 \cdot \cos(30^\circ)
   \]

2. **For \(y\) (opposite side)**:
   \[
   \sin(30^\circ) = \frac{y}{15}
   \]
   Solving for \(y\):
   \[
   y = 15 \cdot \sin(30^\circ)
   \]

Let me calculate these values.

\[
\cos(30^\circ) = \frac{\sqrt{3}}{2} \quad \text{and} \quad \sin(30^\circ) = \frac{1}{2}
\]

Thus:
1. \(x = 15 \times \frac{\sqrt{3}}{2} \approx 15 \times 0.866 = 12.99 \, \text{m}\)
2. \(y = 15 \times \frac{1}{2} = 7.5 \, \text{m}\)

So,
- \(x \approx 12.99 \, \text{m}\)
- \(y = 7.5 \, \text{m}\)

Would you like further details or clarification on the steps?

### Related Questions:
1. How can we verify these trigonometric calculations?
2. What is the total area of the triangle?
3. How do we find the perimeter of the triangle?
4. What is the length of the other angle besides \(30^\circ\)?
5. How do trigonometric functions change for other angles?

**Tip:** Memorizing common angle values like \(30^\circ\), \(45^\circ\), and \(60^\circ\) can speed up problem-solving in geometry.

A right-angled triangle where one angle is 30 degrees, the hypotenuse is 15 meters, and the goal is to find the adjacent (x) and opposite (y) sides using trigonometric ratios.

Learn how to solve for the adjacent (x) and opposite (y) sides of a right triangle with a 30-degree angle and a 15-meter hypotenuse using trigonometric functions like sine and cosine. Suitable for students in Grades 9-11.

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