# trig

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a plane is flying with airspeed of 140 mph and heading 280 degrees. The wind currents are running at 20mph at 260 degrees clockwise from due north. Find the true course and ground speed of the plane.

• trig -

Vp=140mi/h @ 280 deg.,CCW. = Velocity of the plane.

Vw = 20mi/h @ 190 deg.CCW. = Velocity of the wind.

X = hor. = 140cos280 + 20cos190,
X = 24.2 + (-19.7) = 4.5mi/h.

Y = ver. = 140sin280 + 20sin190,
Y = -137.87 + (-3.47) = -141.34mi/h.

tanA = Y/X = -141.34/4.5 = - 31.41,
A = -88.2 deg,CW = 360 - 88.2 = 271.8
deg, CCW. = Direction.

R = X/cosA = 4.5/cos271.8 = 141.4mi/h = Magnatude.

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