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4 December, 04:31

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?

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  1. 4 December, 04:43
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    =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°
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