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