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Math Help - Law of Cosine Word Problems Pt. 2

  1. #1
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    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.
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  2. #2
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    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 P, where \angle NPA = 63^o
    . . and sails 36 miles to point A.

    The second ship leaves the port P, where \angle SPB = 67^o
    . . and sails 48 miles to point B.

    We see that \angle APB = 60^o.


    Law of Cosines: . AB^2 \:=\:36^2 + 48^2 - 2(36)(48)\cos60^o

    Got it?

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