Thread: Trig Question about Bearings

Jason is on a 50m high bridge and sees two boats anchored below. From his position, Boat A has a bearing of 230 degrees and boat B has a bearing of 120 degrees. Jason estimates the angles of depression to be 38 degrees for boat A and 35 degrees for Boat B. How far apart are the boats. Nearest meter.

Im just a bit confused about the bearings part.

Help is appreciated Thanks in advance

Hello, ferken!

This is a 3-D trig problem, but we can work in two dimensions at a time.

Jason is on a 50m high bridge and sees two boats anchored below.
From his position, boat A has a bearing of 230° and boat B has a bearing of 120°.
Jason estimates the angles of depression to be 38° for boat A and 35° for Boat B.
How far apart are the boats (nearest meter)?

Jason looks at boat A.

Code:

      W - - - - - * J
            38° * |
              *   |
            *     | 50
          *       |
        * 38°     |
    A * - - - - - * C

Jason is at
The bridge is:


In right triangle



Jason looks at boat B.

Code:

    J * - - - - E
      | * 35°
      |   *
   50 |     *
      |       *
      |     35° *
    C * - - - - - * B

Jason is at
The bridge is:


In right triangle



Looking down from the sky, this is the diagram:

Code:

                N
                |
                |
                |
               C* 120°
           64 *   *
            *  110° *  71.4
         A*           *
                *       *
                      *   *
                            *B

Law of Cosines: .

Therefore: .