https://file.aiquickdraw.com/mathbot/file/1727376884268o2oe0xjt.jpg

The given image shows a right triangle \( \triangle CHO \), where:
- The hypotenuse \( HO \) is labeled as 11 cm.
- The angle at \( C \) is 44°.
- The right angle is at \( O \).

We are asked to find the side lengths of the triangle and any unknown angles.

### Step-by-Step Solution:
1. **Identify the sides**:
   - \( HO \) is the hypotenuse (11 cm).
   - \( y \) is the side opposite the angle \( 44^\circ \) at \( C \).
   - The side \( CO \) is adjacent to the angle \( 44^\circ \).

2. **Use Trigonometric Ratios**:
   Since this is a right triangle, we can use sine and cosine:
   
   - \( \sin(44^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{y}{11} \)
   - \( \cos(44^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{CO}{11} \)

3. **Solve for \( y \) and \( CO \)**:
   - To find \( y \) (opposite side):  
     \[
     y = 11 \cdot \sin(44^\circ)
     \]
   - To find \( CO \) (adjacent side):  
     \[
     CO = 11 \cdot \cos(44^\circ)
     \]

Let me calculate the exact values for \( y \) and \( CO \).The side lengths of the triangle are approximately:

- \( y \) (opposite the \( 44^\circ \) angle): \( 7.64 \, \text{cm} \)
- \( CO \) (adjacent to the \( 44^\circ \) angle): \( 7.91 \, \text{cm} \)

Would you like further details or clarifications on any part of this problem?

Here are 5 related questions:
1. How would you find the area of this right triangle?
2. What is the third angle of the triangle at \( H \)?
3. Can you use the tangent function to verify the value of \( y \)?
4. How would the side lengths change if the hypotenuse were longer?
5. How do sine and cosine functions relate to each other in a right triangle?

**Tip**: Always check if your results make sense, especially when using trigonometric functions, by ensuring the values are reasonable for the given triangle dimensions.

Find the missing side lengths and angles in the right triangle, given that the hypotenuse is 11 cm, one angle is 44°, and there is a right angle at O.

Learn how to solve a right triangle with a 44° angle and an 11 cm hypotenuse. This problem uses trigonometric ratios (sine and cosine) to find the unknown sides of the triangle. Suitable for students in Grades 9-11.

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