Construct a triangle BCP given BC = 5 cm, BP = 4 cm and `anglePBC=45^(@)`.
Measure and record the length of PC.

Answer

To construct triangle BCP given BC = 5 cm, BP = 4 cm, and angle PBC = 45°, follow these steps:

### Step-by-Step Solution

1. **Draw Line Segment BC:**
- Using a ruler, draw a line segment BC that measures 5 cm. Label the endpoints as B and C.
- **Hint:** Ensure that you measure accurately using the ruler to get a precise length of 5 cm.

2. **Construct Angle PBC:**
- At point B, you need to construct an angle of 45°.
- First, draw a 90° angle at point B. You can do this by using a compass to draw arcs from point B and marking the intersection points.
- Then, bisect the 90° angle to obtain a 45° angle. This can be done by drawing arcs from the points where the 90° angle intersects the lines, and marking the intersection of these arcs.
- **Hint:** The angle bisector will divide the 90° angle into two equal parts, giving you the 45° angle.

3. **Mark Point P:**
- On the line you just drew (the 45° line), measure 4 cm from point B using a ruler and mark this point as P.
- **Hint:** Make sure to keep the ruler aligned with the angle to ensure that you are measuring along the correct direction.

4. **Join Points P and C:**
- Draw a line segment connecting point P to point C.
- **Hint:** Use a ruler to ensure that the line is straight and accurately connects the two points.

5. **Measure Length of PC:**
- Finally, use the ruler to measure the length of segment PC. Record this length.
- **Hint:** Ensure that you measure from the endpoint of P to the endpoint of C for an accurate measurement.

### Conclusion
- After completing the construction, you should find that the length of PC is approximately 3.5 cm.