An airplane with a speed of 160 knots is headed east while a 22-knot wind is blowing from 240°. find the ground speed to the nearest tenth of a knot

181.1 knots

Step-by-step explanation

Blowing from 240º means blowing towards 240 - 180 = 60º.  

Therefore, when we add the two vectors nose-to-tail, the angle between them is 180º - (90º - 60º) = 150º.  

We can use the Law of Cosines:  

x^2 = 160^2 + 24^2 - 2×160×24×cos(150º)  

x^2 = 25600 + 576 - 7680(-sqrt(0.75))  

x = sqrt(26176 + 7680×sqrt(0.75))  

x = 181.1824

  = 181.1 knots

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