Thread: Word bearing Problem

A ship is sailing due north. At a certain point the bearing of a lighthouse is N E and the distance is 12.5. After a while, the captain notices that the bearing of the lighthouse is now S E. How far did the ship travel between the two observations of the lighthouse.

What's the distance?

Hello, qbkr21!

A ship is sailing due north.
At a certain point the bearing of a lighthouse is and the distance is 12.5 (miles?)
After a while, the captain notices that the bearing of the lighthouse is now .
How far did the ship travel between the two observations of the lighthouse?

Code:

    B *
      | *
      |   *
      |42.9°*
      |       *
     c|         *
      |      88.5°* C
      |        *
      |48.6°* b=12.5
      |  *
    A *

At the ship takes a bearing of the lighthouse at
. . and finds angle and miles.

Later at point , they find that angle .
. . Hence, angle

To find side , use the Law of Sines: .

So we have: .

Therefore, the distance is about miles.

Thanks Soroban you are incredible at math. I will learn from this.