Hello, aikenfan!
(31) A ship leaves port at noon and has a bearing of S24°W.
The ship sails at 20 knots.
How many nautical miles south and west will the ship have sailed by 6 pm? Code:
P
*
/|
/ |
/ |
/24°|
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120 / |
/ |
/ |
/ |
* - - - - *
A S
The ship leaves the port $\displaystyle P$ at 12 noon and sails at 20 knots.
. . In 6 hours, it has sailed 120 nautical miles to $\displaystyle A.$
We have: .$\displaystyle \cos24^o \:=\:\frac{PS}{120}\quad\Rightarrow\quad PS \:=\:120\!\cdot\!\cos24^o \:=\:109.6254549$
. . Therefore, the ship sailed about 109.6 nautical miles south.
We have: .$\displaystyle \sin24^o \:=\:\frac{AS}{120}\quad\Rightarrow\quad AS \:=\:120\!\cdot\!\sin24^o \:=\:48.80839717$
. . Therefore, the ship sailed about 48.8 nautical miles west.