We can summarize that
By applying the law of cosines:
c² = a² + b² - 2abcos(C)
where:
a,b, and c represent the triangle's sides and C denotes the angle opposing side c.
Let us assign:
a=170 miles
b=200 miles
c=160 miles
Thus, we establish:
160² = 170² + 200² - 2(170)(200)cos(C).
We now aim to 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).
Thus, cos(C)=0.6367.
C=arc cos(0.6367)--------> C=50.45°.
Consequently, the captain should adjust toward island B by
180 - 50.45 = 129.55 degrees.
The final answer is
129.55 degrees
.
