To solve this problem, we need to establish a few key details based on the provided information.

1. Determine the Bearings

• The bearings of the tangents are:
  • Tangent 1: S76°50'W
  • Tangent 2: N77°00'W

2. Coordinates of Key Points

• Point of Curvature (PC): 50.00 N, 50.00 E
• Point X: 43.88 N, 11.26 E
• Stationing of Vertex: 2 + 972.45 (which translates to 2972.45 meters if the unit is meters)

3. Define the Points

• Point of Tangent (PT): We need to determine this point and the radius of the curve.

4. Analyze the Geometry

• The angle between the two tangents can be calculated as:
  • Angle = (Bearing of Tangent 1) - (Bearing of Tangent 2)
  • Convert bearings to azimuths if necessary.

5. Calculate Radius of the Curve

The radius $R$ can be determined using the formula for circular curves, which relates to the tangent and the distance from the PC to the PT.

6. Compute the Coordinates of Point X in Terms of Stationing

The coordinates of point X can be calculated based on its position relative to PC and the curve properties.

Steps for Calculation

1. Calculate the Angle Between the Tangents:

   • Convert the bearings to degrees and find the internal angle.

2. Determine the Radius:

   • Using the formulas related to circular curves, $R = \frac{L^2}{8D}$ where $L$ is the length of the curve and $D$ is the deflection angle.

3. Find Stationing of PT:

   • Use the stationing of the vertex and add the length of the curve.

4. Determine Stationing of Point X:

   • Based on the curve length and the position of X relative to PC.

Calculations

Let’s perform these calculations step by step.

Step 1: Calculate the Angle Between the Tangents

• Bearing 1: $180° - 76.833° = 103.167°$ (converted to azimuth)
• Bearing 2: $77.000°$
• Angle = $103.167° - 77.000° = 26.167°$

Step 2: Determine the Radius

Assuming you have the arc length $L$ from the stationing information and using the appropriate formulas, you can determine the radius. For simplicity, let's denote:

• $D = 26.167°$

If more specific length data were provided, the calculation for the radius $R$ could be explicitly completed.

Step 3: Find Stationing of PT

Using the arc length and the vertex stationing:

• $\text{Stationing of PT} = \text{Stationing of Vertex} + \text{Arc Length}$

Step 4: Calculate Coordinates of Point X

Using the distance to Point X from PC and the calculated curve parameters.

Final Notes

Without specific arc lengths or additional detail, I can only outline the approach. If you provide the arc length or additional data, I can complete the calculations for you.

Questions

1. Do you have the length of the curve or any additional details?
2. Would you like a specific formula to calculate the radius?
3. Are there any assumptions about the horizontal or vertical alignment that need clarification?
4. Would you like to visualize the curve based on the given coordinates?
5. Do you need help understanding the conversion between bearings and azimuths?

Tip

When dealing with bearings and curves, always ensure your angle measurements are consistent and carefully note the transition between different types of measurements (degrees, radians, etc.).