Solve the problem.
-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 to the nearest tenth of a kilometer.
A)3.1 km
B)3.5 km
C)2.7 km
D)3.7 km

Question

Quizplus · Accepted Answer

To solve this problem, we can use trigonometry, specifically the Law of Sines, in the 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 180° - 73° = 107° (since the ship sailed due west, forming a right angle with the initial bearing line). Using the Law of Sines, we have (sin 42° / 4.7 km) = (sin 107° / distance ship sailed), solving for the distance gives approximately 3.7 km.

Solve the Problem. -It Is 4.7 Km from Lighthouse a to Port B