# Thread: Law of Cosine Word Problems Pt. 2

1. ## 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.

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

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

We see that $\displaystyle \angle APB = 60^o.$

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

Got it?