Math CentralQuandaries & Queries


Question from jane, a student:

a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East then 3.40 km North East, then an additional distance in an unknown direction. Her final position is 6.68 km directly east of the starting point. find the magnitude & direction of the third leg of the voyage.

please help me with this thanks!


Did you draw a diagram?


I have labeled the Beginning point, the First change of direction, the Second change of direction and the End point. Look at triangle SFE. You know |SF| = 2.00 km, |FE| = 6.68 - 2.00 = 4.68 km and the measure of angle SFE is 45o. To solve the problem you need to determine |ES| and the measure of angle ESF. The Law of Cosines and the Law of Sines will help you do this.


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