Math (Trig.)

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A boat sailing from A to B travels in a straight line until the captain realizes he is off course. The boat is turned through an angle of 60 degrees, then travels another 10 km to B. The trip would have been 4 km shorter if the boat had gone straight from A to B. How far did the boat travel?

  • Math (Trig.) -

    Assume that the distance travelled before turning 60 degrees is x
    The total distance travelled = x+10
    Distance A-B in straight line = x + 6

    Use the cosine rule:
    (x+6)^2 = x^2 + 100 - (2*x*10*cos(120))

    Finish the calculation, you'll find x. Total distance travelled will be (x + 10)

  • Math (Trig.) -

    15.8

  • Math (Trig.) -

    32

  • Math (Trig.) -

    32+10=42km

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