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11 November, 15:54

Island A is 210 miles from island B. A ship captain travels 230 miles from island A and then finds that he is off course and 180 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

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  1. 11 November, 16:09
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    He should turn 60° to head straight towards island B.

    Step-by-step explanation:

    Let us assume a Triangle ABC. Where side AB is the distance of the island A and island B and is 210 miles. AC is the wrong Course that a ship took and is 230 miles. CB is the course straight towards island B from C and equals 180 miles.

    Finding angle C:

    Now that the three sides of the triangle are known, we can find the angle that the ship should turn to using the law of cosines:

    Cos C = (a²+b²-c²) / 2ab where c = AB, b = AC, a = BC

    Cos C = (180² + 230² - 210²) / 2*180*230

    C = cos⁻¹ (41200/82800)

    C = cos⁻¹ (0.4976)

    angle C = 60.15

    angle C = 60° approx
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