Physics

An airplane flies at airspeed (relative to the air) of 430 km/h . The pilot wishes to fly due North (relative to the ground) but there is a 43 km/h wind blowing Southwest (direction 225◦).
In what direction should the pilot head the plane (measured clockwise from North)?
Answer in units of degrees.

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  1. 43/√2 = 30.4, so the wind's vector is (-30.4,-30.4)

    If the plane flies on heading θ,

    (-30.4,-30.4)+(430cos(θ-45°),430sin(θ-45°)) = (0,y)

    so, we have -30.4 + 430cos(θ-45) = 0
    cos(θ-45) = 30.4/430 = 4.05

    so, the plane flies N41°E

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  2. is 41 degrees east of north the exact degree number??? because a computer program wants the exact number and i cant round over or under 1%...

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