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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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) About Me  (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:

RED² = GREEN² + BLUE² - 2·GREEN·BLUE·cos(111°)

RED² = 90² + 120² - 2·90·120·cos(111°)

RED² = 30240.74771

 RED = 173.90 miles, rounded to 2 decimal places.

Edwin