SOLUTION: Two ships leave the dock at 8:00 AM. The first ship travels at a bearing of N 26� W at 18 miles per hour. The second ship travels at a bearing of S 43� W at 24 miles per hou

Question 1121026: Two ships leave the dock at 8:00 AM. The first ship travels at a bearing
of N 26� W at 18 miles per hour. The second ship travels at a bearing of
S 43� W at 24 miles per hours. Find the distance between the two ships at
1:00 pm that same day.
Round your answer to two decimal places.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

From 8:00 AM to 1:00 PM is 5 hours.

N 26� W means start North and turn 26� toward West,
S 43� W means start South and turn 43� toward West.

The GREEN line is the path of the first ship.

So the length of the GREEN line is rate�time = 18�5 = 90 miles

The BLUE line is the path of the second ship.

So the length of the BLUE line is rate�time = 24�5 = 120 miles.

The angle between the GREEN and BLUE lines is 180�-26�-43� = 111�

We use the law of cosines to find the RED line:

RED� = GREEN� + BLUE� - 2�GREEN�BLUE�cos(111�)

RED� = 90� + 120� - 2�90�120�cos(111�)

RED� = 30240.74771

 RED = 173.90 miles, rounded to 2 decimal places.

Edwin

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