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We are given a right triangle with:
- Hypotenuse = 2.72 units,
- One angle = \( 29^\circ \),
- One side labeled \( x \) (adjacent to the angle),
- Another side labeled \( y \) (opposite to the angle).

We need to find \( x \) and \( y \).

### Step 1: Find \( x \) Using the Cosine Function

The cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse:

\[
\cos(29^\circ) = \frac{x}{2.72}
\]

Solving for \( x \):

\[
x = 2.72 \cdot \cos(29^\circ)
\]

Using a calculator to find \( \cos(29^\circ) \):

\[
\cos(29^\circ) \approx 0.8746
\]

Now calculate \( x \):

\[
x \approx 2.72 \cdot 0.8746 \approx 2.38 \text{ units}
\]

### Step 2: Find \( y \) Using the Sine Function

The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse:

\[
\sin(29^\circ) = \frac{y}{2.72}
\]

Solving for \( y \):

\[
y = 2.72 \cdot \sin(29^\circ)
\]

Using a calculator to find \( \sin(29^\circ) \):

\[
\sin(29^\circ) \approx 0.4848
\]

Now calculate \( y \):

\[
y \approx 2.72 \cdot 0.4848 \approx 1.32 \text{ units}
\]

### Final Answer:
- \( x \) (adjacent side) is approximately **2.38 units**.
- \( y \) (opposite side) is approximately **1.32 units**.

Would you like more details or have any questions?

### Related Questions:
1. How would the lengths of \( x \) and \( y \) change if the angle was increased to \( 45^\circ \)?
2. How can you verify the value of \( y \) using the tangent function?
3. What is the area of this triangle?
4. How would the hypotenuse change if both \( x \) and \( y \) were doubled?
5. Can you calculate the remaining angle in this triangle?

### Tip:
Using sine and cosine functions makes it easy to find unknown sides when you know one angle and the hypotenuse in a right triangle.

Learn how to solve for the sides x and y in a right triangle with a hypotenuse of 2.72 units and an angle of 29°. This detailed step-by-step guide covers trigonometric concepts like sine and cosine. Suitable for students in Grades 9-12.

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