Island a is 150 miles from island b. a ship captain travels 240 miles from island a and then finds that he is off course and 200 miles from island b. what bearing should he turn to, so he is heading straight towards island b?

We know that
Applying the law of cosines: 

c² = a² + b² - 2abcos(C) 
where: 
a,b and c are sides of the triangle and C is the angle opposite side c 

that is 
150² = 240² + 200² - 2(240)(200)cos(C) 

solve for C 

22,500 = 57,600 + 40,000 - 96,000cos(C) 
22,500-57,600-40,000 = -96,000cos(C) 
-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)> C=38.53°°

hence, 
he should turn in the direction of island b by
180 - 38.53 = 141.47 degrees