# Law of Cosine Word Problems Pt. 2

• Jul 12th 2009, 06:00 PM
jordangiscool
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.
• Jul 12th 2009, 08:47 PM
Soroban
Hello, jordangiscool!

Did you make a sketch?

Quote:

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?