https://file.aiquickdraw.com/mathbot/file/1725758526661reavr52w.jpg

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The image contains a trigonometry-based problem involving a right-angled triangle, labeled with angles and side lengths. Let me break down the problem and work towards a solution.

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The diagram shows:
1. A right-angled triangle with an angle of \(30^\circ\), and a side labeled \(h = 17\).
2. Using trigonometric relationships (likely sine, cosine, or tangent) to solve for the other sides and angles.

I will go through the steps mentioned in the image and explain the solution.From what I can see in the image, here’s the breakdown:

1. **The given information**:
   - A right-angled triangle.
   - Angle \(\theta = 30^\circ\).
   - One side labeled as \(h = 17\) units (presumably the hypotenuse).

2. **Objective**:
   - Find other side lengths and possibly angles using trigonometric ratios (sine, cosine, or tangent).

3. **Key Trigonometric Ratios**:
   For a right triangle, we use:
   - \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)
   - \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
   - \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)

4. **Using the Angle \(30^\circ\)**:
   - \(\sin(30^\circ) = \frac{1}{2}\)
   - \(\cos(30^\circ) = \frac{\sqrt{3}}{2}\)

   With \(h = 17\):
   - The opposite side (relative to \(30^\circ\)) is: 
     \[
     \text{opposite} = h \cdot \sin(30^\circ) = 17 \cdot \frac{1}{2} = 8.5
     \]
   - The adjacent side is:
     \[
     \text{adjacent} = h \cdot \cos(30^\circ) = 17 \cdot \frac{\sqrt{3}}{2} \approx 17 \cdot 0.866 = 14.722
     \]

Thus, the opposite side is \(8.5\) units, and the adjacent side is approximately \(14.722\) units.

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Let me know if you'd like further details or additional clarification! Here are some related questions for practice:

1. What is the relationship between sine and cosine for complementary angles in a right triangle?
2. How would you use the Pythagorean theorem to verify the results?
3. What is the tangent of a \(30^\circ\) angle in this context?
4. How would the side lengths change if the hypotenuse was larger?
5. What are the standard values for sine and cosine at \(45^\circ\)?

**Tip**: Always remember that in a right triangle, the sum of the squares of the two smaller sides equals the square of the hypotenuse.

Find the opposite and adjacent sides of a right triangle where the hypotenuse is 17 units, and one angle is 30 degrees.

Learn how to solve a right triangle where the hypotenuse is 17 units and one angle is 30 degrees. Using trigonometric ratios, we find the opposite and adjacent sides. This is suitable for students in Grades 9-11.

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