PreCalc  Vectors
posted by Joe .
An airplane is flying with an airspeed of 660 Kilometers per hour. The wind is blowing from 345 degrees at 35 km/h. What direction should the airplane take so that, with the wind, the plane will be flying in a direction of 72 degrees?
I can compute airspeed and actual direction using law of sines and cosines but not sure how to figure out the requested 72 degree part.

PreCalc  Vectors 
Henry
X = hor. = 660 + 35cos345 = km/h.
Y = ver. = 35sin345 =
tanA = Y/X = 9.06 / 693.8 = .0131,
A = 0.75 deg.
A + B = 72,
0.75 + B = 72,
B = 72 + 0.75 = 72.75 deg. = Direction. 
PreCalc  Vectors 
Henry
Vpw = Vp + Vw = 660[72o].
Vp + 35[345o] = 660[72].
Vp+35*Cos345+35*sin345=660*Cos72+660*sin72.
Vp + 33.89.1i = 204+627.7i.
Vp=204 + 627.7i 33.8+9.1i=170.2+636.8i
= 659km/h[75o].
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