Assignment:
A ship captain at sea uses a sextant to sight an angle of elevation of 37 degrees to the top of lighthouse. After the ship travels 250 feet directly toward the lighthouse, another sighting is made, and the new angle of elevation is 50 degrees. The ship charts show that there are dangerous rocks 100 feet from the base of the lighthouse. Find to the nearest foot, how close to the rocks the ship is at the time of the second sighting.
Provide complete and step by step solution for the question and show calculations and use formulas.