Question

Island A is 160 miles from island B. A ship captain travels 220 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

Answer:

=135.53°

Step-by-step explanation:

The bearing that the captain should turn is the angle difference between the two islands from the position of the ship.

Let C be the position of the ship, then

AB is c=160

AC is b=220

BC is a=200

We use the cosine rule as follows:

c²=a²+b²-2ab Cos C

160²=200²+220²-2×200×220 Cos C

25600=88400-88000Cos C

88000 Cos C=88400-25600

88000Cos C=62800

Divide both sides by 88000.

Cos C=62800/88000

=0.7136

C=44.47°

He should turn (180°-44.47°)=135.53°