Question

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?

Answer 1

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