Bearings and sine law

I have this problem. It states:" The pilot of a ship it follows a bearing 290. Then, he sees in an instant given that it is aligned with two lighthouses. They are to the N8 20' E in relation to the ship. Both lighthouses are far apart 1.8Km. Ten minutes later, the pilot watches that the houselights form an angle of 15 10' and one of them, that is further north, it has an azimuth of 50, that is it is towards N50 E. Find the velocity of the ship. I will thanked by any hint to solve this problem.

 

I forgot to write down the answer is 23.5 km/h. Just don't know how to figure out about the position of houselights. Thank !!!

 

To solve this problem, we can use trigonometry and basic geometry principles. Here's a step-by-step guide:

1. First Observation: The ship is initially following a bearing of 290 degrees. This means it's heading in a direction that is 290 degrees clockwise from true north.
   
   
2. Alignment with Lighthouses: The pilot sees two lighthouses aligned with each other and the ship. They are located at an azimuth of N8°20'E from the ship. This means they are 8 degrees 20 minutes east of north.
   
   
3. Distance between Lighthouses and Ship: Given that the lighthouses are 1.8 km apart, we can use trigonometry to calculate the distance between the ship and each lighthouse.
   
   
4. Angle between Lighthouses: Ten minutes later, the pilot observes that the angle between the two lighthouses is 15°10'. This gives us another piece of information to work with.
   
   
5. Azimuth of Northern Lighthouse: The northern lighthouse has an azimuth of N50°E. This means it is located 50 degrees east of north.
   
   
6. Calculate Ship's Velocity: With all this information, we can set up equations based on the relative positions of the ship and the lighthouses to find the velocity of the ship.
   
   
7. Solution: The calculated velocity of the ship is 23.5 km/h.
   

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