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The problem provided asks for the distance between two ships L and G, both of which have known bearings from a lighthouse and are a certain distance from an oil rig.

### Problem Recap:
1. **Bearings**:
   - Ship L has a bearing of 320° from the lighthouse.
   - Ship G has a bearing of 285° from the lighthouse.

2. **Position relative to oil rig**:
   - Both ships are due north of the oil rig.
   - The oil rig is 15.2 nautical miles due west of the lighthouse.

### Steps to Solve:

1. **Determine the positions of the ships** relative to the lighthouse using trigonometry.
2. **Calculate the difference** in position between the two ships to find the distance.

Let's start by establishing a coordinate system with the lighthouse at the origin (0, 0). 

### Coordinates of the Ships:

1. **Ship L** (using bearing 320°):
   - \( x_L = r \cos(320°) \)
   - \( y_L = r \sin(320°) \)
   - Since the distance (r) from the oil rig to the lighthouse is 15.2 nautical miles and both ships are directly north of the oil rig, the actual bearing will help define the positions relative to the oil rig's coordinates.
  
2. **Ship G** (using bearing 285°):
   - \( x_G = r \cos(285°) \)
   - \( y_G = r \sin(285°) \)
   - The same reasoning applies here to establish coordinates relative to the oil rig.

3. **Final Calculation**:
   - Use the distance formula to find the distance \( d \) between the two ships:
   \[
   d = \sqrt{(x_G - x_L)^2 + (y_G - y_L)^2}
   \]
   
I'll proceed to calculate these now.The distance between the two ships, L and G, is approximately **9.1 nautical miles**.

Would you like more details on the calculations, or do you have any further questions?

### Related Questions:
1. How do bearings relate to angles in standard trigonometry?
2. What would the distance be if the ships were at different bearings?
3. How can we determine the bearing if only the coordinates are given?
4. How does the distance from the oil rig affect the distance between the ships?
5. What would the effect be if one ship was south of the oil rig instead of north?

**Tip:** When working with bearings, always remember that they are measured clockwise from the north, which can sometimes require converting the angle to match standard trigonometric directions.

Calculate the distance between ships L and G using their known bearings from a lighthouse and the position of an oil rig. This problem involves applying trigonometric principles, specifically the distance formula, to determine spatial relationships. Suitable for advanced high school students.

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