Construct a right-angled triangle whose hypotenuse measures 5.6 cm and one of whose acute angles measures `30^(@)`.

Answer

To construct a right-angled triangle with a hypotenuse measuring 5.6 cm and one of the acute angles measuring 30 degrees, follow these steps:

### Step-by-Step Solution:

1. **Draw the Hypotenuse:**
- Use a ruler to draw a line segment AC that measures 5.6 cm. This will be the hypotenuse of the triangle.
- Label the endpoints as A and C.

**Hint:** Make sure to measure accurately using the ruler to ensure the length is exactly 5.6 cm.

2. **Construct the Right Angle:**
- At point A, use a protractor to measure a right angle (90 degrees). Draw a line segment AB perpendicular to AC.

**Hint:** Place the center of the protractor at point A and align one edge of the protractor with line AC to measure the 90-degree angle.

3. **Construct the 30-degree Angle:**
- At point C, use the protractor to measure a 30-degree angle from line AC. Draw a line segment CD that makes a 30-degree angle with AC.

**Hint:** Ensure the protractor is aligned correctly with line AC to accurately measure the 30 degrees.

4. **Locate Point B:**
- The lines AB and CD will intersect at point B. Mark this intersection point as B.

**Hint:** Make sure to extend lines AB and CD sufficiently so that they intersect clearly.

5. **Complete the Triangle:**
- Now, you have triangle ABC where:
- AC is the hypotenuse (5.6 cm),
- Angle A is 60 degrees (since 90 + 30 = 120, and 180 - 120 = 60),
- Angle B is 90 degrees,
- Angle C is 30 degrees.

**Hint:** Double-check the angles using the protractor to ensure they are correct.

### Summary of Steps:
- Draw hypotenuse AC = 5.6 cm.
- Construct a right angle at A.
- Construct a 30-degree angle at C.
- Mark the intersection as point B to complete triangle ABC.