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In the given image, you have a right-angled triangle where:

- The hypotenuse is 20 meters.
- One of the angles is 30°.
- The side opposite the 30° angle is labeled \( y \).
- The adjacent side to the 30° angle is labeled \( x \).

We can use basic trigonometry to find \( x \) and \( y \).

1. **To find \( y \) (opposite side):**

Using the sine function:
\[
\sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{y}{20}
\]

\[
y = 20 \times \sin(30^\circ)
\]

Since \( \sin(30^\circ) = 0.5 \):
\[
y = 20 \times 0.5 = 10 \, \text{meters}
\]

2. **To find \( x \) (adjacent side):**

Using the cosine function:
\[
\cos(30^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{x}{20}
\]

\[
x = 20 \times \cos(30^\circ)
\]

Since \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866 \):
\[
x = 20 \times 0.866 = 17.32 \, \text{meters}
\]

Thus:
- \( y = 10 \, \text{meters} \)
- \( x = 17.32 \, \text{meters} \)

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:
1. How do we calculate the area of this triangle?
2. What would happen if the angle was 45° instead of 30°?
3. Can you find the perimeter of the triangle?
4. What other trigonometric functions can we use to solve for \( x \) and \( y \)?
5. How would the results change if the hypotenuse were 30 meters?

**Tip:** When solving right triangles, remember that sine and cosine functions are useful for opposite and adjacent sides, respectively, while tangent relates both sides directly.

What are the values of x and y in a right triangle with a hypotenuse of 20 meters and an angle of 30°?

Learn how to calculate the opposite and adjacent sides of a right triangle with a 30° angle and a 20-meter hypotenuse. This solution involves using sine and cosine trigonometric functions. Suitable for students in Grades 9-11.

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