Question

22.Island A is 160 miles from island B. A ship captain travels 170 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 

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