Posted by Joe on Tuesday, May 3, 2011 at 12:00am.
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, Wednesday, May 4, 2011 at 7:12pm
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, Sunday, August 2, 2015 at 8:19pm
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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