Math Help - Law of Cosine Word Problems Pt. 2

Two ships leave a port at 9 A.M. One travels at a bearing of N 53 degrees W at 12 mph and the other travels at a bearing of S 67 degrees W at 16 mph. Approximate how far apart they are at noon that day.

Hello, jordangiscool!

Did you make a sketch?

Two ships leave a port at 9 A.M.
One travels at a bearing of N 53° W at 12 mph
and the other travels at a bearing of S 67° W at 16 mph.
Approximate how far apart they are at noon that day.

Code:

              A *       N
               /  *     |
              /  36 *53°|
             /        * |
            /       60° * P
           /         *  |
          /   48  * 67° |
         /     *        |
        /   *           S
       / *
    B *

The first ship leaves the port , where
. . and sails 36 miles to point

The second ship leaves the port , where
. . and sails 48 miles to point

We see that


Law of Cosines: .

Got it?