Choose the one alternative that best completes the statement or answers the question.
-It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has the ship sailed from the port?
Round your answer to the nearest 0.1 km.
A) 3.5 km
B) 3.7 km
C) 3.1 km
D) 2.7 km

Question

Quizplus · Accepted Answer

To solve this problem, we can use trigonometry, specifically the Law of Sines, in a triangle formed by the lighthouse, the port, and the ship's current position. The angle at the lighthouse is 73° - 31° = 42°, and the angle at the port is 90° (since the ship sailed due west, forming a right angle). We can then set up the equation using the Law of Sines: (4.7 / sin(42°)) = (distance from port to ship / sin(90°)). Solving for the distance gives approximately 3.7 km.

Choose the One Alternative That Best Completes the Statement or Answers