a simple curve is to be run joining two tangents of bearings s76°50′w and n77°00′w and is to pass a point x of coordinates 43.88n and 11.26e. if the coordinates of pc are 50.00n and 50.00e and the stationing of vertex is 2+972.45, find the radius of the curve, the stationing of pt and the stationing of point x.

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.).

A simple curve is to be run joining two tangents of bearings S76°50′W and N77°00′W and is to pass a point X of coordinates 43.88N and 11.26E. If the coordinates of PC are 50.00N and 50.00E and the stationing of vertex is 2+972.45, find the radius of the curve, the stationing of PT, and the stationing of point X.

Explore how to calculate the radius of a curve and the stationing of points based on bearings S76°50′W and N77°00′W, with specific coordinates for PC and point X. This problem involves key geometric concepts and formulas relevant for advanced mathematics.

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