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