Question 1121026
{{{drawing(400,400,-100,100,-100,100,
locate(3,100,N), locate(-6,-95,S), locate(100,-3,E),locate(-95,10,W),
line(-120,0,120,0), line(0,-120,0,120),
green(line(0,0,-39.45,80.89)),blue(line(0,0,-81.84,-87.76)),
arc(0,0,80,-80,90,116), locate(-12,35,"26°"),
arc(0,0,80,-80,227,270), locate(-17,-30,"43°"),

arc(0,0,50,-50,116,227),locate(-20,9,"111°"),
green(locate(-20,50,90)), blue(locate(-50,-50,120)),


red(line(-39.45,80.89,-81.84,-87.76)) )}}}
<pre>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</pre>