Certainly! Here’s how you can implement the calculation in Python:

```python
import numpy as np

# Define the site point and the unit vector
site_A = np.array([x, y, z])
unit_vector_A = np.array([ux, uy, uz])  # Replace ux, uy, uz with actual values

# Compute the new point on the line
x_line = site_A[0] + unit_vector_A[0]
y_line = site_A[1] + unit_vector_A[1]
z_line = site_A[2] + unit_vector_A[2]

# Create the vector for the line
line_vector = np.array([x_line, y_line, z_line])

# Normalize the unit vector to ensure it's a unit vector
unit_vector = unit_vector_A / np.linalg.norm(unit_vector_A)

# Calculate the angle with the z-axis (North Pole)
dot_product_z = np.dot(unit_vector, np.array([0, 0, 1]))
magnitude_unit_vector = np.linalg.norm(unit_vector)
theta = np.arccos(dot_product_z / magnitude_unit_vector)  # Angle with z-axis in radians

# Convert radians to degrees
theta_degrees = np.degrees(theta)

# Calculate the angle from the horizontal plane
dot_product_xy = np.dot(unit_vector[:2], np.array([1, 0]))  # Project onto the x-axis
phi = np.arccos(np.linalg.norm(unit_vector[:2]) / magnitude_unit_vector)  # Angle from xy-plane in radians

# Convert radians to degrees
phi_degrees = np.degrees(phi)

print(f"Angle with the North Pole: {theta_degrees:.2f} degrees")
print(f"Angle from the horizontal plane: {phi_degrees:.2f} degrees")
```

### Explanation:
1. **Vector Setup**: Define `site_A` and `unit_vector_A`.
2. **Line Point Calculation**: Compute the point on the line using the site and the unit vector.
3. **Normalization**: Ensure the `unit_vector` is normalized.
4. **Angle Calculation**:
   - **Angle with the z-axis** (`theta`): Use the dot product and magnitudes.
   - **Angle from the horizontal plane** (`phi`): Calculate the projection and use the cosine relationship.

### How to Use:
- Replace `x`, `y`, `z`, `ux`, `uy`, `uz` with actual numeric values.
- Run the script to get the angles in degrees.

Feel free to ask if you have more questions or need further assistance!

Learn how to calculate angles using vectors and Python with a detailed step-by-step guide. This problem covers key concepts in vector mathematics, including dot products, unit vectors, and angle conversions. Suitable for advanced high school students and beyond.

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