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?