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In the given right triangle, we are provided with:

- Hypotenuse = 20
- Angle = 30°
- We are to solve for \(x\) (the opposite side) and \(y\) (the adjacent side).

We will use trigonometric functions to solve for both \(x\) and \(y\).

1. **To find \(x\) (the side opposite the 30° angle)**:
   \[
   \sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{x}{20}
   \]
   Solving for \(x\):
   \[
   x = 20 \times \sin(30^\circ)
   \]

2. **To find \(y\) (the side adjacent to the 30° angle)**:
   \[
   \cos(30^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{y}{20}
   \]
   Solving for \(y\):
   \[
   y = 20 \times \cos(30^\circ)
   \]

Now, let me calculate the values of \(x\) and \(y\).The solutions for the triangle are:

- \(x \approx 10\) (opposite side)
- \(y \approx 17.32\) (adjacent side)

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

Here are 5 related questions for further exploration:
1. How would the values of \(x\) and \(y\) change if the angle were 45°?
2. Can you solve for the area of this right triangle using the values of \(x\) and \(y\)?
3. How would you use the Pythagorean theorem to check your results for \(x\) and \(y\)?
4. How do trigonometric ratios change as the angle increases or decreases in a right triangle?
5. What other angles could be used in this triangle, and how would that affect the side lengths?

**Tip:** In any right triangle, knowing one angle and the hypotenuse is enough to find all side lengths using trigonometric functions!

Solve for the lengths of the sides x and y of a right triangle using trigonometric functions. The triangle has a hypotenuse of 20 units and an angle of 30°. Learn to use sine and cosine to find unknown sides. Suitable for Grades 8-10.

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