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
let
a=170 mi
b=200 mi
c=160 mi
that is
160² = 170² + 200² - 2(170)(200)cos(C)
solve for C
25,600 = 28,900 + 40,000 - 68,000cos(C)
25,600 - 28,900 - 40,000 = -68,000cos(C)
-43,300=-68,000cos (C)
cos (C)=0.6367
C=arc cos(0.6367)--------> C=50.45°
hence,
he should turn in the direction of island b by
180 - 50.45 = 129.55 degrees
the answer is
129.55 degrees
